ModuleCurveModel_nonempty_iso_unit_of_eulerChar_sectionsOf_eq_of_ratFunc.lean
Nyll.JacobianVarieties.Picard.CurveModel_nonempty_iso_unit_of_eulerChar_sectionsOf_eq_of_ratFunc
6 declarations indexed from sourceView source ↗ Module documentation
Line bundles of degree zero on a rational curve
Divisor presentations compute Euler characteristics on rational curve models. An invertible module with the Euler characteristic of the unit module is trivial; the corresponding pullback criterion is obtained from the same computation.
Declarations
JacobianVarieties.Picard.Proofs.RationalEulerUnit.AlgebraicGeometry.TwoGluedProjectiveLines.S2e.exists_divisor_presentation_forall_eulerChar_eq_degree_add_one
Source context 39 commands
Surrounding namespaces, section variables, and local commands at this declaration.
section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.RationalEulerUnit
attribute [-instance]
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
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.instHasLocalResidue_of_hasCanonicalLocalResidueK
AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
attribute [-instance]
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
AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
AlgebraicGeometry.isClosedImmersion_graphOver
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
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
attribute [-instance]
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.RelEffCartierDiv.subsingleton_of_degree_zero
SheafOfModules.isIso_ihomModelToIhom AlgebraicGeometry.OModulePresheaf.isScalarTower
AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
AlgebraicGeometry.OModulePresheaf.module AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
AlgebraicGeometry.OModulePresheaf.addCommGroup
AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
AlgebraicGeometry.OModulePresheaf.moduleSections
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
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
attribute [-instance]
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 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
attribute [-simp]
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 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
attribute [-simp]
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 AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
AlgebraicCurve.TranscendenceTower.mk.injEq AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec AlgebraicCurve.PoleDivisorPackage.mk.injEq
AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
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.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.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.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 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
attribute [-simp]
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 PresheafOfModules.freeεIso_hom_app
PresheafOfModules.freeμIso_hom_app AlgebraicGeometry.prodKerGraph_one
AlgebraicGeometry.fibrePowOver.proj_comp AlgebraicGeometry.prodKerGraph_zero
AlgebraicGeometry.RelEffCartierDiv.empty_I AlgebraicGeometry.fibrePowOver.proj_comp_assoc
AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec AlgebraicCurve.SymmetricPowerPackage.mk.injEq
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.tensorPow_zero
attribute [-simp]
AlgebraicGeometry.Scheme.Modules.tensorPow_succ
AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.mk.injEq
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.Hom.mk.injEq AlgebraicGeometry.OModulePresheaf.Hom.id_app
AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
AlgebraicGeometry.OModulePresheaf.AffHom.id_app
AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.Hom.comp_app AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq AlgebraicGeometry.OModulePresheaf.prod_obj
AlgebraicGeometry.OModulePresheaf.restrOpen_obj
AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
AlgebraicGeometry.OModulePresheaf.pushforward_obj AlgebraicGeometry.OModulePresheaf.im_obj
AlgebraicGeometry.OModulePresheaf.pow_obj AlgebraicGeometry.OModulePresheaf.fstHom_app
AlgebraicGeometry.OModulePresheaf.ker_obj AlgebraicGeometry.OModulePresheaf.coker_obj
AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
attribute [-simp]
AlgebraicGeometry.OModulePresheaf.sndHom_app
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 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.SubPicGroupCondition.mk.injEq
AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
GoodReductionJacobian.relativeGroupLawOfGrpObj_one
GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
universe u
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.MonoidalCategory
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.AlgebraicCurve hiding genus
open _root_.AlgebraicCurve hiding genus
namespace AlgebraicGeometry
open _root_.AlgebraicGeometry
namespace TwoGluedProjectiveLines
namespace S2e
open _root_.AlgebraicGeometry
open _root_.AlgebraicCurve hiding genus
Lean source · full declarationtheorem exists_divisor_presentation_forall_eulerChar_eq_degree_add_one
(k : Type u) [Field k] [IsAlgClosed k] (M : CurveModel k (RatFunc k))
(N : M.C.Modules) (hN : Scheme.Modules.IsInvertible N) :
let : Algebra k M.C.functionField :=
(AlgebraicCurve.baseToFunctionField M.toBase).toAlgebra
∃ (D : AlgebraicCurve.Divisor k M.C.functionField)
(φ : ∀ U : M.C.Opens, Γ(N, U) →+ (M.C.functionField : Type u)),
(∀ (U V : M.C.Opens) (h : V ≤ U), Nonempty V →
∀ m : Γ(N, U), φ V (N.presheaf.map (homOfLE h).op m) = φ U m) ∧
(∀ (U : M.C.Opens) [Nonempty U] (a : Γ(M.C, U)) (m : Γ(N, U)),
φ U (a • m) = algebraMap Γ(M.C, U) M.C.functionField a * φ U m) ∧
(∀ U : M.C.Opens, Nonempty U → Function.Injective (φ U)) ∧
(∀ U : M.C.Opens, IsAffineOpen U → Nonempty U →
Set.range (φ U) =
(AlgebraicCurve.lSpaceOn (AlgebraicCurve.placesOf M.toBase U) D :
Set M.C.functionField)) ∧
∀ 𝒲 : M.C.TwoAffineOpenCover,
Module.Finite k (𝒲.sectionsOf M.toBase N).H0 ∧
Module.Finite k (𝒲.sectionsOf M.toBase N).H1 ∧
(Module.finrank k (𝒲.sectionsOf M.toBase N).H0 : ℤ) -
Module.finrank k (𝒲.sectionsOf M.toBase N).H1 =
AlgebraicCurve.Divisor.degree D + 1 := by
intro functionFieldAlgebra
obtain ⟨D, φ, hnat, hsmul, hinj, hrange, -⟩ :=
Scheme.Modules.IsInvertible.exists_divisor_range_eq_lSpaceOn M.toBase N hN
refine ⟨D, φ, hnat, hsmul, hinj, hrange, fun 𝒲 => ?_⟩
obtain ⟨hf0, hf1, -, -, hχ⟩ :=
AlgebraicCurve.finrank_H0_H1_sectionsOf_of_range_eq_lSpaceOn
𝒲 M.toBase N D φ hnat hsmul hinj hrange
obtain ⟨φ₀, -, hnat₀, hsmul₀, hinj₀, hrange₀⟩ :=
Scheme.Modules.exists_unit_range_eq_lSpaceOn_zero M.toBase
obtain ⟨-, -, -, -, hχ₀⟩ :=
AlgebraicCurve.finrank_H0_H1_sectionsOf_of_range_eq_lSpaceOn 𝒲 M.toBase
(SheafOfModules.unit M.C.ringCatSheaf : M.C.Modules) 0 φ₀ hnat₀ hsmul₀ hinj₀ hrange₀
obtain ⟨h1, h0⟩ :=
AlgebraicCurve.CurveModel.finrank_H1_sectionsOf_unit_eq_zero_and_finrank_H0_eq_one_of_ratFunc
k M 𝒲
rw [h1, h0, map_zero] at hχ₀
refine ⟨hf0, hf1, ?_⟩
rw [hχ]
push_cast at hχ₀ ⊢
linarith
JacobianVarieties.Picard.Proofs.RationalEulerUnit.AlgebraicGeometry.TwoGluedProjectiveLines.S2e.exists_int_forall_eulerChar_sectionsOf_eq_add_one
Source context 39 commands
Surrounding namespaces, section variables, and local commands at this declaration.
section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.RationalEulerUnit
attribute [-instance]
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
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.instHasLocalResidue_of_hasCanonicalLocalResidueK
AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
attribute [-instance]
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
AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
AlgebraicGeometry.isClosedImmersion_graphOver
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
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
attribute [-instance]
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.RelEffCartierDiv.subsingleton_of_degree_zero
SheafOfModules.isIso_ihomModelToIhom AlgebraicGeometry.OModulePresheaf.isScalarTower
AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
AlgebraicGeometry.OModulePresheaf.module AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
AlgebraicGeometry.OModulePresheaf.addCommGroup
AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
AlgebraicGeometry.OModulePresheaf.moduleSections
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
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
attribute [-instance]
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 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
attribute [-simp]
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 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
attribute [-simp]
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 AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
AlgebraicCurve.TranscendenceTower.mk.injEq AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec AlgebraicCurve.PoleDivisorPackage.mk.injEq
AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
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.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.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.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 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
attribute [-simp]
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 PresheafOfModules.freeεIso_hom_app
PresheafOfModules.freeμIso_hom_app AlgebraicGeometry.prodKerGraph_one
AlgebraicGeometry.fibrePowOver.proj_comp AlgebraicGeometry.prodKerGraph_zero
AlgebraicGeometry.RelEffCartierDiv.empty_I AlgebraicGeometry.fibrePowOver.proj_comp_assoc
AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec AlgebraicCurve.SymmetricPowerPackage.mk.injEq
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.tensorPow_zero
attribute [-simp]
AlgebraicGeometry.Scheme.Modules.tensorPow_succ
AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.mk.injEq
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.Hom.mk.injEq AlgebraicGeometry.OModulePresheaf.Hom.id_app
AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
AlgebraicGeometry.OModulePresheaf.AffHom.id_app
AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.Hom.comp_app AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq AlgebraicGeometry.OModulePresheaf.prod_obj
AlgebraicGeometry.OModulePresheaf.restrOpen_obj
AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
AlgebraicGeometry.OModulePresheaf.pushforward_obj AlgebraicGeometry.OModulePresheaf.im_obj
AlgebraicGeometry.OModulePresheaf.pow_obj AlgebraicGeometry.OModulePresheaf.fstHom_app
AlgebraicGeometry.OModulePresheaf.ker_obj AlgebraicGeometry.OModulePresheaf.coker_obj
AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
attribute [-simp]
AlgebraicGeometry.OModulePresheaf.sndHom_app
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 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.SubPicGroupCondition.mk.injEq
AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
GoodReductionJacobian.relativeGroupLawOfGrpObj_one
GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
universe u
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.MonoidalCategory
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.AlgebraicCurve hiding genus
open _root_.AlgebraicCurve hiding genus
namespace AlgebraicGeometry
open _root_.AlgebraicGeometry
namespace TwoGluedProjectiveLines
namespace S2e
open _root_.AlgebraicGeometry
open _root_.AlgebraicCurve hiding genus
JacobianVarieties.Picard.Proofs.RationalEulerUnit.AlgebraicGeometry.TwoGluedProjectiveLines.S2e.nonempty_iso_unit_iff_eq_zero_of_forall_eulerChar_eq
Source context 39 commands
Surrounding namespaces, section variables, and local commands at this declaration.
section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.RationalEulerUnit
attribute [-instance]
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
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.instHasLocalResidue_of_hasCanonicalLocalResidueK
AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
attribute [-instance]
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
AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
AlgebraicGeometry.isClosedImmersion_graphOver
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
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
attribute [-instance]
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.RelEffCartierDiv.subsingleton_of_degree_zero
SheafOfModules.isIso_ihomModelToIhom AlgebraicGeometry.OModulePresheaf.isScalarTower
AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
AlgebraicGeometry.OModulePresheaf.module AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
AlgebraicGeometry.OModulePresheaf.addCommGroup
AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
AlgebraicGeometry.OModulePresheaf.moduleSections
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
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
attribute [-instance]
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 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
attribute [-simp]
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 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
attribute [-simp]
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 AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
AlgebraicCurve.TranscendenceTower.mk.injEq AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec AlgebraicCurve.PoleDivisorPackage.mk.injEq
AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
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.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.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.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 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
attribute [-simp]
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 PresheafOfModules.freeεIso_hom_app
PresheafOfModules.freeμIso_hom_app AlgebraicGeometry.prodKerGraph_one
AlgebraicGeometry.fibrePowOver.proj_comp AlgebraicGeometry.prodKerGraph_zero
AlgebraicGeometry.RelEffCartierDiv.empty_I AlgebraicGeometry.fibrePowOver.proj_comp_assoc
AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec AlgebraicCurve.SymmetricPowerPackage.mk.injEq
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.tensorPow_zero
attribute [-simp]
AlgebraicGeometry.Scheme.Modules.tensorPow_succ
AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.mk.injEq
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.Hom.mk.injEq AlgebraicGeometry.OModulePresheaf.Hom.id_app
AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
AlgebraicGeometry.OModulePresheaf.AffHom.id_app
AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.Hom.comp_app AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq AlgebraicGeometry.OModulePresheaf.prod_obj
AlgebraicGeometry.OModulePresheaf.restrOpen_obj
AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
AlgebraicGeometry.OModulePresheaf.pushforward_obj AlgebraicGeometry.OModulePresheaf.im_obj
AlgebraicGeometry.OModulePresheaf.pow_obj AlgebraicGeometry.OModulePresheaf.fstHom_app
AlgebraicGeometry.OModulePresheaf.ker_obj AlgebraicGeometry.OModulePresheaf.coker_obj
AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
attribute [-simp]
AlgebraicGeometry.OModulePresheaf.sndHom_app
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 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.SubPicGroupCondition.mk.injEq
AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
GoodReductionJacobian.relativeGroupLawOfGrpObj_one
GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
universe u
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.MonoidalCategory
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.AlgebraicCurve hiding genus
open _root_.AlgebraicCurve hiding genus
namespace AlgebraicGeometry
open _root_.AlgebraicGeometry
namespace TwoGluedProjectiveLines
namespace S2e
open _root_.AlgebraicGeometry
open _root_.AlgebraicCurve hiding genus
JacobianVarieties.Picard.Proofs.RationalEulerUnit.AlgebraicGeometry.TwoGluedProjectiveLines.S2e.exists_int_forall_eulerChar_pullback_eq_add_one
Source context 39 commands
Surrounding namespaces, section variables, and local commands at this declaration.
section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.RationalEulerUnit
attribute [-instance]
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
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.instHasLocalResidue_of_hasCanonicalLocalResidueK
AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
attribute [-instance]
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
AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
AlgebraicGeometry.isClosedImmersion_graphOver
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
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
attribute [-instance]
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.RelEffCartierDiv.subsingleton_of_degree_zero
SheafOfModules.isIso_ihomModelToIhom AlgebraicGeometry.OModulePresheaf.isScalarTower
AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
AlgebraicGeometry.OModulePresheaf.module AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
AlgebraicGeometry.OModulePresheaf.addCommGroup
AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
AlgebraicGeometry.OModulePresheaf.moduleSections
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
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
attribute [-instance]
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 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
attribute [-simp]
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 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
attribute [-simp]
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 AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
AlgebraicCurve.TranscendenceTower.mk.injEq AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec AlgebraicCurve.PoleDivisorPackage.mk.injEq
AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
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.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.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.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 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
attribute [-simp]
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 PresheafOfModules.freeεIso_hom_app
PresheafOfModules.freeμIso_hom_app AlgebraicGeometry.prodKerGraph_one
AlgebraicGeometry.fibrePowOver.proj_comp AlgebraicGeometry.prodKerGraph_zero
AlgebraicGeometry.RelEffCartierDiv.empty_I AlgebraicGeometry.fibrePowOver.proj_comp_assoc
AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec AlgebraicCurve.SymmetricPowerPackage.mk.injEq
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.tensorPow_zero
attribute [-simp]
AlgebraicGeometry.Scheme.Modules.tensorPow_succ
AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.mk.injEq
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.Hom.mk.injEq AlgebraicGeometry.OModulePresheaf.Hom.id_app
AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
AlgebraicGeometry.OModulePresheaf.AffHom.id_app
AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.Hom.comp_app AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq AlgebraicGeometry.OModulePresheaf.prod_obj
AlgebraicGeometry.OModulePresheaf.restrOpen_obj
AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
AlgebraicGeometry.OModulePresheaf.pushforward_obj AlgebraicGeometry.OModulePresheaf.im_obj
AlgebraicGeometry.OModulePresheaf.pow_obj AlgebraicGeometry.OModulePresheaf.fstHom_app
AlgebraicGeometry.OModulePresheaf.ker_obj AlgebraicGeometry.OModulePresheaf.coker_obj
AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
attribute [-simp]
AlgebraicGeometry.OModulePresheaf.sndHom_app
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 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.SubPicGroupCondition.mk.injEq
AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
GoodReductionJacobian.relativeGroupLawOfGrpObj_one
GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
universe u
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.MonoidalCategory
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.AlgebraicCurve hiding genus
open _root_.AlgebraicCurve hiding genus
namespace AlgebraicGeometry
open _root_.AlgebraicGeometry
namespace TwoGluedProjectiveLines
namespace S2e
open _root_.AlgebraicGeometry
open _root_.AlgebraicCurve hiding genus
JacobianVarieties.Picard.Proofs.RationalEulerUnit.AlgebraicGeometry.TwoGluedProjectiveLines.S2e.nonempty_pullback_iso_pullback_unit_iff_eq_zero
Source context 39 commands
Surrounding namespaces, section variables, and local commands at this declaration.
section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.RationalEulerUnit
attribute [-instance]
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
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.instHasLocalResidue_of_hasCanonicalLocalResidueK
AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
attribute [-instance]
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
AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
AlgebraicGeometry.isClosedImmersion_graphOver
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
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
attribute [-instance]
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.RelEffCartierDiv.subsingleton_of_degree_zero
SheafOfModules.isIso_ihomModelToIhom AlgebraicGeometry.OModulePresheaf.isScalarTower
AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
AlgebraicGeometry.OModulePresheaf.module AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
AlgebraicGeometry.OModulePresheaf.addCommGroup
AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
AlgebraicGeometry.OModulePresheaf.moduleSections
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
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
attribute [-instance]
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 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
attribute [-simp]
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 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
attribute [-simp]
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 AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
AlgebraicCurve.TranscendenceTower.mk.injEq AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec AlgebraicCurve.PoleDivisorPackage.mk.injEq
AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
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.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.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.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 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
attribute [-simp]
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 PresheafOfModules.freeεIso_hom_app
PresheafOfModules.freeμIso_hom_app AlgebraicGeometry.prodKerGraph_one
AlgebraicGeometry.fibrePowOver.proj_comp AlgebraicGeometry.prodKerGraph_zero
AlgebraicGeometry.RelEffCartierDiv.empty_I AlgebraicGeometry.fibrePowOver.proj_comp_assoc
AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec AlgebraicCurve.SymmetricPowerPackage.mk.injEq
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.tensorPow_zero
attribute [-simp]
AlgebraicGeometry.Scheme.Modules.tensorPow_succ
AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.mk.injEq
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.Hom.mk.injEq AlgebraicGeometry.OModulePresheaf.Hom.id_app
AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
AlgebraicGeometry.OModulePresheaf.AffHom.id_app
AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.Hom.comp_app AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq AlgebraicGeometry.OModulePresheaf.prod_obj
AlgebraicGeometry.OModulePresheaf.restrOpen_obj
AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
AlgebraicGeometry.OModulePresheaf.pushforward_obj AlgebraicGeometry.OModulePresheaf.im_obj
AlgebraicGeometry.OModulePresheaf.pow_obj AlgebraicGeometry.OModulePresheaf.fstHom_app
AlgebraicGeometry.OModulePresheaf.ker_obj AlgebraicGeometry.OModulePresheaf.coker_obj
AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
attribute [-simp]
AlgebraicGeometry.OModulePresheaf.sndHom_app
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 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.SubPicGroupCondition.mk.injEq
AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
GoodReductionJacobian.relativeGroupLawOfGrpObj_one
GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
universe u
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.MonoidalCategory
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.AlgebraicCurve hiding genus
open _root_.AlgebraicCurve hiding genus
namespace AlgebraicGeometry
open _root_.AlgebraicGeometry
namespace TwoGluedProjectiveLines
namespace S2e
open _root_.AlgebraicGeometry
open _root_.AlgebraicCurve hiding genus
AlgebraicCurve.CurveModel.nonempty_iso_unit_of_eulerChar_sectionsOf_eq_of_ratFunc
Source context 34 commands
Surrounding namespaces, section variables, and local commands at this declaration.
section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.RationalEulerUnit
attribute [-instance]
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
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.instHasLocalResidue_of_hasCanonicalLocalResidueK
AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
attribute [-instance]
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
AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
AlgebraicGeometry.isClosedImmersion_graphOver
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
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
attribute [-instance]
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.RelEffCartierDiv.subsingleton_of_degree_zero
SheafOfModules.isIso_ihomModelToIhom AlgebraicGeometry.OModulePresheaf.isScalarTower
AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
AlgebraicGeometry.OModulePresheaf.module AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
AlgebraicGeometry.OModulePresheaf.addCommGroup
AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
AlgebraicGeometry.OModulePresheaf.moduleSections
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
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
attribute [-instance]
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 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
attribute [-simp]
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 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
attribute [-simp]
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 AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
AlgebraicCurve.TranscendenceTower.mk.injEq AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec AlgebraicCurve.PoleDivisorPackage.mk.injEq
AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
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.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.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.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 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
attribute [-simp]
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 PresheafOfModules.freeεIso_hom_app
PresheafOfModules.freeμIso_hom_app AlgebraicGeometry.prodKerGraph_one
AlgebraicGeometry.fibrePowOver.proj_comp AlgebraicGeometry.prodKerGraph_zero
AlgebraicGeometry.RelEffCartierDiv.empty_I AlgebraicGeometry.fibrePowOver.proj_comp_assoc
AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec AlgebraicCurve.SymmetricPowerPackage.mk.injEq
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.tensorPow_zero
attribute [-simp]
AlgebraicGeometry.Scheme.Modules.tensorPow_succ
AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.mk.injEq
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.Hom.mk.injEq AlgebraicGeometry.OModulePresheaf.Hom.id_app
AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
AlgebraicGeometry.OModulePresheaf.AffHom.id_app
AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.Hom.comp_app AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq AlgebraicGeometry.OModulePresheaf.prod_obj
AlgebraicGeometry.OModulePresheaf.restrOpen_obj
AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
AlgebraicGeometry.OModulePresheaf.pushforward_obj AlgebraicGeometry.OModulePresheaf.im_obj
AlgebraicGeometry.OModulePresheaf.pow_obj AlgebraicGeometry.OModulePresheaf.fstHom_app
AlgebraicGeometry.OModulePresheaf.ker_obj AlgebraicGeometry.OModulePresheaf.coker_obj
AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
attribute [-simp]
AlgebraicGeometry.OModulePresheaf.sndHom_app
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 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.SubPicGroupCondition.mk.injEq
AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
GoodReductionJacobian.relativeGroupLawOfGrpObj_one
GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
universe u
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.MonoidalCategory
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.AlgebraicCurve hiding genus
open _root_.AlgebraicCurve hiding genus
open AlgebraicGeometry.TwoGluedProjectiveLines.S2e in