NYLL
Module

RelativeGroupLaw_endDegree_nsmul_idPoint_eq_pow_of_natCast_ne_zero.lean

Nyll.JacobianVarieties.Picard.RelativeGroupLaw_endDegree_nsmul_idPoint_eq_pow_of_natCast_ne_zero
47 declarations indexed from sourceView source ↗

Module documentation

The degree of multiplication on an abelian scheme

On a commutative abelian scheme of relative dimension g over an algebraically closed field, multiplication by a natural number n has endomorphism degree n ^ (2 * g) when the image of n in the field is nonzero.

Imports32
Imported by3

Declarations

theorem

compT_mul

L619 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.compT_mul
Source context 51 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
section Points
variable (L : RelativeGroupLaw K f)
Lean source · statement
theorem compT_mul {T : Scheme.{u}} {t : T ⟶ Spec (CommRingCat.of K)} (z : SchemeHomOver t f)
    (β δ : SchemeHomOver f f) :
    z ⊚ (L.mul f β δ) = L.mul t (z ⊚ β) (z ⊚ δ)
theorem

compT_one

L628 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.compT_one
Source context 51 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
section Points
variable (L : RelativeGroupLaw K f)
Lean source · statement
theorem compT_one {T : Scheme.{u}} {t : T ⟶ Spec (CommRingCat.of K)} (z : SchemeHomOver t f) :
    z ⊚ (L.one f) = L.one t
theorem

pow_eq_nsmul

L636 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.pow_eq_nsmul
Source context 51 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
section Points
variable (L : RelativeGroupLaw K f)
Lean source · full declaration
theorem pow_eq_nsmul {T : Scheme.{u}} (t : T ⟶ Spec (CommRingCat.of K)) (x : SchemeHomOver t f)
    (n : ℕ) :
    let _ : Group (SchemeHomOver t f) := L.pointGroup t; x ^ n = L.nsmul t n x := by
  intro pointGroup
  induction n with
  | zero => rfl
  | succ n ih => rw [pow_succ, ih]; rfl
theorem

comp_idPoint

L644 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.comp_idPoint
Source context 51 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
section Points
variable (L : RelativeGroupLaw K f)
Lean source · statement
theorem comp_idPoint {T : Scheme.{u}} {t : T ⟶ Spec (CommRingCat.of K)} (x : SchemeHomOver t f) :
    x ⊚ (RelativeGroupLaw.idPoint (f := f)) = x
theorem

isHom_nsmul

L648 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.isHom_nsmul
Source context 51 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
section Points
variable (L : RelativeGroupLaw K f)
Lean source · statement
theorem isHom_nsmul (hc : L.IsCommutative) (n : ℕ) {T : Scheme.{u}}
    (t : T ⟶ Spec (CommRingCat.of K))
    (x y : SchemeHomOver t f) :
    (L.mul t x y) ⊚ (L.nsmul f n RelativeGroupLaw.idPoint) =
      L.mul t (x ⊚ L.nsmul f n RelativeGroupLaw.idPoint) (y ⊚ L.nsmul f n RelativeGroupLaw.idPoint)
theorem

isCommMonObj

L671 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.isCommMonObj
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
Lean source · full declaration
theorem isCommMonObj (L : RelativeGroupLaw K f) (hc : L.IsCommutative) :
    let _ : GrpObj (Over.mk f) := L.grpObjOverMk; IsCommMonObj (Over.mk f) :=
  (L.isCommMonObj_grpObjOverMk_iff_mul_comm).mpr (fun t x y => hc t x y)
theorem

geometricallyConnected

L675 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.geometricallyConnected
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
Lean source · statement
theorem geometricallyConnected [IsAlgClosed K]
    (hA : AbelianSchemePropertyBundle K f) :
    GeometricallyConnected f
def

unbundleHom

L685 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.unbundleHom
Documentation

The group homomorphism from endomorphisms in the over category to relative self-morphisms.

Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
Lean source · full declaration
def unbundleHom (L : RelativeGroupLaw K f) :
    let _ : GrpObj (Over.mk f) := L.grpObjOverMk
    let _ : Group (SchemeHomOver f f) := L.pointGroup f;
    (Over.mk f ⟶ Over.mk f) →* SchemeHomOver f f := by
  intro groupObject pointGroup
  exact
    { toFun := overHomToSchemeHomOver
      map_one' := L.overHomToSchemeHomOver_one f
      map_mul' := fun a b => L.overHomToSchemeHomOver_mul f a b }
theorem

toOverHom_idPoint

L695 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.toOverHom_idPoint
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
Lean source · statement
theorem toOverHom_idPoint : schemeHomOverToOverHom (RelativeGroupLaw.idPoint (f := f)) = 𝟙 (Over.mk
  f)
theorem

left_one_zpow_natCast

L699 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.left_one_zpow_natCast
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
Lean source · full declaration
theorem left_one_zpow_natCast (L : RelativeGroupLaw K f) (n : ℕ) :
    let _ : GrpObj (Over.mk f) := L.grpObjOverMk;
    ((𝟙 (Over.mk f)) ^ (n : ℤ)).left = (L.nsmul f n RelativeGroupLaw.idPoint).1 := by
  intro groupObject
  let _ : Group (SchemeHomOver f f) := L.pointGroup f
  rw [zpow_natCast]
  have h := map_pow (unbundleHom L) (𝟙 (Over.mk f)) n
  change overHomToSchemeHomOver ((𝟙 (Over.mk f)) ^ n) = (overHomToSchemeHomOver (𝟙 (Over.mk f))) ^
    n at h
  rw [← toOverHom_idPoint, overHomToSchemeHomOver_schemeHomOverToOverHom, pow_eq_nsmul L f] at h
  rw [toOverHom_idPoint] at h
  exact congrArg Subtype.val h
theorem

left_one_inv

L712 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.left_one_inv
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
Lean source · full declaration
theorem left_one_inv (L : RelativeGroupLaw K f) :
    let _ : GrpObj (Over.mk f) := L.grpObjOverMk;
    ((𝟙 (Over.mk f))⁻¹).left = (L.inv f RelativeGroupLaw.idPoint).1 := by
  intro groupObject
  have h := L.overHomToSchemeHomOver_inv f (𝟙 (Over.mk f))
  rw [← toOverHom_idPoint, overHomToSchemeHomOver_schemeHomOverToOverHom] at h
  rw [toOverHom_idPoint] at h
  exact congrArg Subtype.val h
theorem

cls_tensor

L725 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.cls_tensor
Source context 51 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
section Skel
variable {C : Type*} [Category C] [MonoidalCategory C]
Lean source · statement
theorem cls_tensor (X Y : C) : toSkeleton (X ⊗ Y) = toSkeleton X * toSkeleton Y
theorem

cls_unit

L728 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.cls_unit
Source context 51 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
section Skel
variable {C : Type*} [Category C] [MonoidalCategory C]
Lean source · statement
theorem cls_unit : toSkeleton (𝟙_ C) = (1 : Skeleton C)
theorem

cls_tensorPow

L732 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.cls_tensorPow
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
Lean source · statement
theorem cls_tensorPow {Z : Scheme.{u}} (N : Z.Modules) (n : ℕ) :
    toSkeleton (N.tensorPow n) = toSkeleton N ^ n
theorem

exists_orderedAffineCover

L738 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.exists_orderedAffineCover
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
Lean source · statement
theorem exists_orderedAffineCover (hf : IsProper f) : Nonempty A.OrderedAffineCover
theorem

eulerChar_congr

L760 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.eulerChar_congr
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
Lean source · statement
theorem eulerChar_congr {M M' : A.Modules} (e : M ≅ M') (𝒦 : A.OrderedAffineCover) :
    (OModulePresheaf.ofModules f M).eulerChar 𝒦 = (OModulePresheaf.ofModules f M').eulerChar 𝒦
def

dil

L778 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.dil
Documentation

Rescale the variable of a rational polynomial by multiplying its i-th coefficient by c to the i-th power.

Source context 51 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
section Alg
open _root_.Polynomial
Lean source · statement
def dil (q : ℚ[X]) (c : ℚ) : ℚ[X]
theorem

dil_eval

L780 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.dil_eval
Source context 51 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
section Alg
open _root_.Polynomial
Lean source · statement
theorem dil_eval (q : ℚ[X]) (c m : ℚ) : (dil q c).eval m = q.eval (c * m)
theorem

dil_coeff

L786 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.dil_coeff
Source context 51 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section V1
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
local infixl:80 " ⊚ " => NeronModelInfra.schemeHomOverComp
section Alg
open _root_.Polynomial
Lean source · statement
theorem dil_coeff (q : ℚ[X]) (c : ℚ) (g : ℕ) : (dil q c).coeff g = c ^ g * q.coeff g
theorem

eulerChar_eq_of_equiv

L807 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.eulerChar_eq_of_equiv
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section Chi
variable {R : Type u} [CommRing R]
Lean source · statement
theorem eulerChar_eq_of_equiv {V V' : Scheme.{u}} {π : V ⟶ Spec (.of R)} {π' : V' ⟶ Spec (.of R)}
    (F : OModulePresheaf π) (F' : OModulePresheaf π') (K : V.OrderedAffineCover) (K' :
      V'.OrderedAffineCover)
    (hcard : Fintype.card K.ι = Fintype.card K'.ι)
    (h0 : Nonempty (F.H0 K ≃ₗ[R] F'.H0 K')) (hs : ∀ i : ℕ, Nonempty (F.HSucc K i ≃ₗ[R] F'.HSucc K'
      i)) :
    F.eulerChar K = F'.eulerChar K'
theorem

eulerChar_ofModules_congr

L822 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.eulerChar_ofModules_congr
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section Chi
variable {R : Type u} [CommRing R]
Lean source · statement
theorem eulerChar_ofModules_congr {V : Scheme.{u}} {π π' : V ⟶ Spec (.of R)} (h : π = π')
    (X : V.Modules)
    (K : V.OrderedAffineCover) : (ofModules π X).eulerChar K = (ofModules π' X).eulerChar K
theorem

preimage_eq_bot

L833 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.preimage_eq_bot
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section PushUnit
variable {R : Type u} [CommRing R] {V Z : Scheme.{u}} (π : V ⟶ Spec (.of R)) (ι : Z ⟶ V)
Lean source · statement
theorem preimage_eq_bot (U : V.Opens) (hU : (U : Set V) = ∅) : ι ⁻¹ᵁ U = ⊥
theorem

subsingleton_sections_of_eq_bot

L842 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.subsingleton_sections_of_eq_bot
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section PushUnit
variable {R : Type u} [CommRing R] {V Z : Scheme.{u}} (π : V ⟶ Spec (.of R)) (ι : Z ⟶ V)
Lean source · statement
theorem subsingleton_sections_of_eq_bot (W : Z.Opens) (h : W = ⊥) : Subsingleton Γ(Z, W)
theorem

supportedIn_top

L846 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.supportedIn_top
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section PushUnit
variable {R : Type u} [CommRing R] {V Z : Scheme.{u}} (π : V ⟶ Spec (.of R)) (ι : Z ⟶ V)
Lean source · statement
theorem supportedIn_top : (pushforwardUnit π ι).SupportedIn ⊤
theorem

res_rfl

L850 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.res_rfl
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section PushUnit
variable {R : Type u} [CommRing R] {V Z : Scheme.{u}} (π : V ⟶ Spec (.of R)) (ι : Z ⟶ V)
Lean source · statement
theorem res_rfl (W : Z.Opens) (x : Γ(Z, W)) : Z.presheaf.map (homOfLE (le_refl W)).op x = x
theorem

appLE_rfl_apply

L853 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.appLE_rfl_apply
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section PushUnit
variable {R : Type u} [CommRing R] {V Z : Scheme.{u}} (π : V ⟶ Spec (.of R)) (ι : Z ⟶ V)
Lean source · statement
theorem appLE_rfl_apply (U : V.Opens) (a : Γ(V, U)) : ι.appLE U (ι ⁻¹ᵁ U) le_rfl a = ι.app U a
theorem

isCoherent

L857 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.isCoherent
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section PushUnit
variable {R : Type u} [CommRing R] {V Z : Scheme.{u}} (π : V ⟶ Spec (.of R)) (ι : Z ⟶ V)
Lean source · statement
theorem isCoherent [IsFinite ι] : (pushforwardUnit π ι).IsCoherent
theorem

loc_core

L868 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.loc_core
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section PushUnit
variable {R : Type u} [CommRing R] {V Z : Scheme.{u}} (π : V ⟶ Spec (.of R)) (ι : Z ⟶ V)
Lean source · statement
theorem loc_core [IsAffineHom ι] (U : V.affineOpens) (g : Γ(Z, ι ⁻¹ᵁ U.1)) (W' : Z.Opens)
    (hle : W' ≤ ι ⁻¹ᵁ U.1)
    (hW' : W' = Z.basicOpen g) :
    (∀ x : Γ(Z, W'), ∃ (n : ℕ) (y : Γ(Z, ι ⁻¹ᵁ U.1)),
        Z.presheaf.map (homOfLE hle).op y = Z.presheaf.map (homOfLE hle).op (g ^ n) * x) ∧
      (∀ y : Γ(Z, ι ⁻¹ᵁ U.1), Z.presheaf.map (homOfLE hle).op y = 0 → ∃ n : ℕ, g ^ n * y = 0)
theorem

preimage_basicOpen_eq

L891 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.preimage_basicOpen_eq
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section PushUnit
variable {R : Type u} [CommRing R] {V Z : Scheme.{u}} (π : V ⟶ Spec (.of R)) (ι : Z ⟶ V)
Lean source · statement
theorem preimage_basicOpen_eq (U : V.affineOpens) (f : Γ(V, U.1)) :
    ι ⁻¹ᵁ V.basicOpen f = Z.basicOpen (ι.appLE U.1 (ι ⁻¹ᵁ U.1) le_rfl f)
theorem

pre_le

L895 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.pre_le
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section PushUnit
variable {R : Type u} [CommRing R] {V Z : Scheme.{u}} (π : V ⟶ Spec (.of R)) (ι : Z ⟶ V)
Lean source · statement
theorem pre_le (U : V.affineOpens) (f : Γ(V, U.1)) : ι ⁻¹ᵁ V.basicOpen f ≤ ι ⁻¹ᵁ U.1
theorem

smul_basicOpen

L898 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.smul_basicOpen
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section PushUnit
variable {R : Type u} [CommRing R] {V Z : Scheme.{u}} (π : V ⟶ Spec (.of R)) (ι : Z ⟶ V)
Lean source · full declaration
theorem smul_basicOpen (U : V.affineOpens) (f : Γ(V, U.1)) (a : Γ(V, U.1))
    (x : Γ(Z, ι ⁻¹ᵁ V.basicOpen f)) :
    ((V.presheaf.map (homOfLE (V.basicOpen_le f)).op).hom a •
        (show (pushforwardUnit π ι).obj (V.basicOpen f) from x)) =
      (show (pushforwardUnit π ι).obj (V.basicOpen f) from
        Z.presheaf.map (homOfLE (pre_le ι U f)).op (ι.appLE U.1 (ι ⁻¹ᵁ U.1) le_rfl a) * x) := by
  change ι.appLE (V.basicOpen f) (ι ⁻¹ᵁ V.basicOpen f) le_rfl ((V.presheaf.map (homOfLE
    (V.basicOpen_le f)).op) a) * x
    = _
  congr 1
  rw [← CommRingCat.comp_apply, ← CommRingCat.comp_apply, Scheme.Hom.map_appLE,
    Scheme.Hom.appLE_map]
theorem

smul_top

L911 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.smul_top
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section PushUnit
variable {R : Type u} [CommRing R] {V Z : Scheme.{u}} (π : V ⟶ Spec (.of R)) (ι : Z ⟶ V)
Lean source · full declaration
theorem smul_top (U : V.affineOpens) (a : Γ(V, U.1)) (y : Γ(Z, ι ⁻¹ᵁ U.1)) :
    (a • (show (pushforwardUnit π ι).obj U.1 from y)) =
      (show (pushforwardUnit π ι).obj U.1 from ι.appLE U.1 (ι ⁻¹ᵁ U.1) le_rfl a * y) := rfl
theorem

res_eq

L915 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.res_eq
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section PushUnit
variable {R : Type u} [CommRing R] {V Z : Scheme.{u}} (π : V ⟶ Spec (.of R)) (ι : Z ⟶ V)
Lean source · full declaration
theorem res_eq (U : V.affineOpens) (f : Γ(V, U.1)) (y : Γ(Z, ι ⁻¹ᵁ U.1)) :
    (pushforwardUnit π ι).res (V.basicOpen_le f) (show (pushforwardUnit π ι).obj U.1 from y) =
      (show (pushforwardUnit π ι).obj (V.basicOpen f) from Z.presheaf.map (homOfLE (pre_le ι U
        f)).op y) := by
  change Z.presheaf.map _ y = _
  rw [Subsingleton.elim (homOfLE ((Opens.map ι.base).monotone (V.basicOpen_le f))) (homOfLE (pre_le
    ι U f))]
theorem

isQuasicoherent

L923 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.isQuasicoherent
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section PushUnit
variable {R : Type u} [CommRing R] {V Z : Scheme.{u}} (π : V ⟶ Spec (.of R)) (ι : Z ⟶ V)
Lean source · statement
theorem isQuasicoherent [IsAffineHom ι] : (pushforwardUnit π ι).IsQuasicoherent
theorem

finrank_comp_iso

L957 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.finrank_comp_iso
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section Rank
variable {R : Type u} [CommRing R] {V Z : Scheme.{u}} (π : V ⟶ Spec (.of R)) (ι : Z ⟶ V)
Lean source · statement
theorem finrank_comp_iso {X Y Y' : Scheme.{u}} (g : X ⟶ Y) [Flat g] [IsFinite g] (e : Y ≅ Y')
    (z : Y') :
    Scheme.Hom.finrank (g ≫ e.hom) z = Scheme.Hom.finrank g (e.inv.base z)
theorem

rankAtStalk_pushforwardUnit_obj

L964 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.rankAtStalk_pushforwardUnit_obj
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section Rank
variable {R : Type u} [CommRing R] {V Z : Scheme.{u}} (π : V ⟶ Spec (.of R)) (ι : Z ⟶ V)
Lean source · statement
theorem rankAtStalk_pushforwardUnit_obj [IsFinite ι] [Flat ι] (U : V.affineOpens) (r : ℕ)
    (hr : ∀ y : V, Scheme.Hom.finrank ι y = r) (𝔭 : PrimeSpectrum Γ(V, U.1)) :
    Module.rankAtStalk (R := Γ(V, U.1)) ((pushforwardUnit π ι).obj U.1) 𝔭 = r
theorem

connectedSpace

L1003 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.connectedSpace
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section Setup
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
Lean source · statement
theorem connectedSpace (hA : AbelianSchemePropertyBundle K f) : ConnectedSpace A
theorem

krullDim_top_le

L1010 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.krullDim_top_le
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section Setup
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
Lean source · statement
theorem krullDim_top_le (g : ℕ) [SmoothOfRelativeDimension g f] :
    topologicalKrullDim ((⊤ : Closeds A) : Set A) ≤ g
theorem

exists_chart_prime

L1015 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.exists_chart_prime
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section Setup
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
Lean source · statement
theorem exists_chart_prime [IsIntegral A] [Nonempty A] (𝒦 : A.OrderedAffineCover) :
    ∃ (U₀ : A.affineOpens) (𝔭 : PrimeSpectrum Γ(A, U₀.1)), (∃ i, U₀.1 = 𝒦.U i) ∧ 𝔭.asIdeal = ⊥
theorem

isInvertible_tensorPow

L1030 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.isInvertible_tensorPow
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section Chain
variable {K : Type u} [Field K] {A : Scheme.{u}} (f : A ⟶ Spec (CommRingCat.of K))
Lean source · statement
theorem isInvertible_tensorPow {𝓛 : A.Modules} (h𝓛 : Scheme.Modules.IsInvertible 𝓛) (n : ℕ) :
    Scheme.Modules.IsInvertible (𝓛.tensorPow n)
theorem

eulerChar_twist_eq

L1041 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.eulerChar_twist_eq
Source context 51 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section Chain
variable {K : Type u} [Field K] {A : Scheme.{u}} (f : A ⟶ Spec (CommRingCat.of K))
variable [IsSeparated f] (𝒦 : A.OrderedAffineCover) (𝓛 : A.Modules) (h𝓛 :
  Scheme.Modules.IsInvertible 𝓛)
  (γ : SchemeHomOver f f) [IsAffineHom γ.1]
include h𝓛 in
Lean source · statement
theorem eulerChar_twist_eq (m : ℕ) :
    ((pushforwardUnit f γ.1).twist (𝓛.tensorPow m)).eulerChar 𝒦 =
      (ofModules f (((Scheme.Modules.pullback γ.1).obj 𝓛).tensorPow m)).eulerChar 𝒦
theorem

coeff_eq_endDegree_mul_coeff

L1091 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.Isog.coeff_eq_endDegree_mul_coeff
Source context 50 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
namespace Isog
open AlgebraicGeometry.OModulePresheaf
section ProjIsog
variable (K : Type u) [Field K] {A : Scheme.{u}} (f : A ⟶ Spec (CommRingCat.of K))
  (L : RelativeGroupLaw K f) (hA : AbelianSchemePropertyBundle K f)
  (g : ℕ) [SmoothOfRelativeDimension g f]
  (𝒦 : A.OrderedAffineCover) (𝓛 : A.Modules) (h𝓛 : Scheme.Modules.IsInvertible 𝓛)
  (γ : SchemeHomOver f f)
  (hγ : ∀ {T : Scheme.{u}} (t : T ⟶ Spec (CommRingCat.of K)) (x y : SchemeHomOver t f),
    NeronModelInfra.schemeHomOverComp (L.mul t x y) γ =
      L.mul t (NeronModelInfra.schemeHomOverComp x γ) (NeronModelInfra.schemeHomOverComp y γ))
  (hfin : IsFinite (L.endKerStr γ))
  (p q : Polynomial ℚ)
  (hp : ∀ m : ℕ, ((OModulePresheaf.ofModules f
      (((Scheme.Modules.pullback γ.1).obj 𝓛).tensorPow m)).eulerChar 𝒦 : ℚ) = p.eval (m : ℚ))
  (hq : ∀ m : ℕ, ((OModulePresheaf.ofModules f (𝓛.tensorPow m)).eulerChar 𝒦 : ℚ) = q.eval (m : ℚ))
include hA hγ hfin hp hq h𝓛 in
Lean source · statement
theorem coeff_eq_endDegree_mul_coeff : p.coeff g = (L.endDegree γ : ℚ) * q.coeff g
theorem

locallyOfFinitePresentation_of_field

L1133 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.locallyOfFinitePresentation_of_field
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section Tail
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
section EtaleKernel
Lean source · statement
theorem locallyOfFinitePresentation_of_field (q : A ⟶ Spec (CommRingCat.of K))
    [LocallyOfFiniteType q] : LocallyOfFinitePresentation q
theorem

etale_endKerStr_nsmul

L1143 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.etale_endKerStr_nsmul
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section Tail
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
section EtaleKernel
Lean source · statement
theorem etale_endKerStr_nsmul (L : RelativeGroupLaw K f) (hc : L.IsCommutative)
    [LocallyOfFiniteType f] (n : ℕ) (hn : (n : K) ≠ 0) :
    Etale (L.endKerStr (L.nsmul f n RelativeGroupLaw.idPoint))
theorem

isFinite_endKerStr_nsmul

L1170 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.isFinite_endKerStr_nsmul
Source context 49 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section Tail
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
section EtaleKernel
Lean source · statement
theorem isFinite_endKerStr_nsmul [IsAlgClosed K] (L : RelativeGroupLaw K f) (hc : L.IsCommutative)
    (hA : AbelianSchemePropertyBundle K f) (n : ℕ) (hn : (n : K) ≠ 0) :
    IsFinite (L.endKerStr (L.nsmul f n RelativeGroupLaw.idPoint))
theorem

main

L1190 ↗
JacobianVarieties.Picard.Proofs.MultiplicationDegree.P2mDegNIsog.main
Source context 52 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.MultiplicationDegree
attribute [-instance]
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
attribute [-instance]
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance]
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-instance]
  instTopologicallyFGOfFiniteType
  AlgebraicGeometry.ProjSpace.twistObj.addCommGroup
  AlgebraicGeometry.ProjSpace.twistFam.module
  AlgebraicGeometry.ProjSpace.twistObj.module
  AlgebraicGeometry.ProjSpace.twistObj.moduleSections
  AlgebraicGeometry.ProjSpace.twistFam.addCommGroup
attribute [-simp]
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
attribute [-simp]
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
attribute [-simp]
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
attribute [-simp]
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
attribute [-simp]
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
attribute [-simp]
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
  RegularLocalRingQuotientAscent.dualNumberFst_apply
  AlgebraicGeometry.ProjSpace.twistObj.mk.injEq
  AlgebraicGeometry.ProjSpace.twistObj.zero_val
  AlgebraicGeometry.ProjSpace.twistObj.add_val
  AlgebraicGeometry.ProjSpace.twist_res_val
  AlgebraicGeometry.ProjSpace.twist_smul_val
  AlgebraicGeometry.ProjSpace.twistGradeToObj_val
  AlgebraicGeometry.ProjSpace.twistObj.smul_val
  AlgebraicGeometry.ProjSpace.twistGradeEquiv_apply_val
  AlgebraicGeometry.ProjSpace.twistObj.mk.sizeOf_spec
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open TopologicalSpace Opposite
universe u
namespace P2mDegNIsog
section Tail
open scoped CategoryTheory.MonObj
variable {K : Type u} [Field K] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of K)}
section Main
variable [IsAlgClosed K] (L : RelativeGroupLaw K f) (hc : L.IsCommutative) (hA :
  AbelianSchemePropertyBundle K f)
  (g : ℕ) [SmoothOfRelativeDimension g f]
include hc hA
open GoodReductionJacobian.RelativeGroupLaw in
Lean source · statement
theorem main (n : ℕ) (hn : (n : K) ≠ 0) :
    L.endDegree (L.nsmul f n RelativeGroupLaw.idPoint) = n ^ (2 * g)
theorem

endDegree_nsmul_idPoint_eq_pow_of_natCast_ne_zero

L1255 ↗
GoodReductionJacobian.RelativeGroupLaw.endDegree_nsmul_idPoint_eq_pow_of_natCast_ne_zero
Documentation

Multiplication by a nonzero natural scalar has degree the scalar to twice the dimension.

Source context 12 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace GoodReductionJacobian.RelativeGroupLaw
noncomputable section
open _root_.JacobianVarieties.Picard.Proofs.MultiplicationDegree
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open _root_.TopologicalSpace _root_.Opposite
universe u
Lean source · statement
theorem endDegree_nsmul_idPoint_eq_pow_of_natCast_ne_zero
    (K : Type u) [Field K] [IsAlgClosed K] {A : Scheme.{u}} (f : A ⟶ Spec (CommRingCat.of K))
    (L : RelativeGroupLaw K f) (hc : L.IsCommutative) (hA : AbelianSchemePropertyBundle K f)
    (g : ℕ) [SmoothOfRelativeDimension g f] (n : ℕ) (hn : (n : K) ≠ 0) :
    L.endDegree (L.nsmul f n RelativeGroupLaw.idPoint) = n ^ (2 * g)

Statements and documentation are read from the Lean source at the revision shown. Source entries are not a measure of mathematical completeness.