Module

AbelianSchemePropertyBundle_geometricallyIntegral_of_commRing.lean

Nyll.AlgebraicCurves.Geometry.AbelianSchemes.Theorems.AbelianSchemePropertyBundle_geometricallyIntegral_of_commRing
1 declaration indexed from sourceView source ↗

Abelian Scheme Property Bundle geometrically Integral of comm Ring

Declarations

GoodReductionJacobian.AbelianSchemePropertyBundle.geometricallyIntegral_of_commRing
Source context 6 commands

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

section ProofImplementation
namespace AlgebraicCurves.Geometry.AbelianSchemes.Theorems.Proofs
namespace AbelianSchemePropertyBundle_geometricallyIntegral_of_commRing
attribute [-simp] GoodReductionJacobian.RelativeGroupLaw.baseChangePointToBase_ofBase
  GoodReductionJacobian.RelativeGroupLaw.baseChangePointToBase_coe
  GoodReductionJacobian.RelativeGroupLaw.baseChangePointOfBase_coe
  GoodReductionJacobian.RelativeGroupLaw.baseChange_inv
  GoodReductionJacobian.RelativeGroupLaw.baseChangePointOfBase_toBase
  GoodReductionJacobian.RelativeGroupLaw.baseChange_mul
  GoodReductionJacobian.RelativeGroupLaw.baseChange_one
  GoodReductionJacobian.RelativeGroupLaw.nsmul_zero
  GoodReductionJacobian.RelativeGroupLaw.mem_torsionSubset
  GoodReductionJacobian.RelativeGroupLaw.nsmul_succ NeronModelInfra.schemeHomOverComp_id_left
  NeronModelInfra.schemeHomOverComp_id_right NeronModelInfra.schemeHomOverId_coe
  NeronModelInfra.schemeHomOverComp_coe NeronModelInfra.fibreRestrictAlong_coe_comp_snd
  NeronModelInfra.fibreRestrictAlong_coe_comp_fst GoodReductionJacobian.RelativeGroupLaw.fibre_inv
  GoodReductionJacobian.RelativeGroupLaw.fibrePointToBase_coe
  GoodReductionJacobian.RelativeGroupLaw.fibrePointOfBase_toBase
  GoodReductionJacobian.RelativeGroupLaw.fibre_mul
  GoodReductionJacobian.RelativeGroupLaw.fibrePointToBase_ofBase
  GoodReductionJacobian.RelativeGroupLaw.fibre_one
  GoodReductionJacobian.RelativeGroupLaw.fibrePointOfBase_coe AlgebraicGeometry.schemeFibreEndo_snd
  AlgebraicGeometry.schemeFibreEndo_fst
universe u
open CategoryTheory CategoryTheory.Limits AlgebraicGeometry NeronModelInfra GoodReductionJacobian
theorem _root_.GoodReductionJacobian.AbelianSchemePropertyBundle.geometricallyIntegral_of_commRing
    {R : Type u} [CommRing R] {A : Scheme.{u}} {f : A ⟶ Spec (CommRingCat.of R)}
    (hA : AbelianSchemePropertyBundle R f) : GeometricallyIntegral f