theorem
L94 ↗exists_isUniversal
AlgebraicGeometry.RelEffCartierDiv.exists_isUniversal
Source context 7 commands
Surrounding namespaces, section variables, and local commands at this declaration.
section ProofImplementation
namespace AlgebraicCurves.RelativeDivisors.Proofs.RelEffCartierDiv_exists_isUniversal
attribute [-instance]
AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
AlgebraicGeometry.isClosedImmersion_graphOver
AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
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
instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
attribute [-simp]
AlgebraicGeometry.prodKerGraph_one
AlgebraicGeometry.fibrePowOver.proj_comp
AlgebraicGeometry.prodKerGraph_zero
AlgebraicGeometry.RelEffCartierDiv.empty_I
AlgebraicGeometry.fibrePowOver.proj_comp_assoc
AlgebraicGeometry.graphOver_fst_assoc
AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
AlgebraicGeometry.graphOver_fst
AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
AlgebraicGeometry.graphOver_snd
AlgebraicGeometry.graphOver_snd_assoc
AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
AlgebraicCurve.SymmetricPowerPackage.mk.injEq
AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
universe u
open CategoryTheory CategoryTheory.Limits Opposite AlgebraicGeometry
open AlgebraicGeometry _root_.AlgebraicGeometry.RelEffCartierDiv inLean source · statement
theorem _root_.AlgebraicGeometry.RelEffCartierDiv.exists_isUniversal
{𝒞 S : Scheme.{u}} (f : 𝒞 ⟶ S) [IsSeparated f] [SmoothOfRelativeDimension 1 f]
(hcov : ∀ (V : S.affineOpens) (F : Finset 𝒞), (∀ x ∈ F, f x ∈ (V : S.Opens)) →
∃ U : 𝒞.Opens, IsAffineOpen U ∧ U ≤ f ⁻¹ᵁ (V : S.Opens) ∧ ∀ x ∈ F, x ∈ U)
(r : ℕ) :
∃ (Y : Scheme.{u}) (y : Y ⟶ S) (Duniv : RelEffCartierDiv f r y), Duniv.IsUniversal