AlgebraicGeometry.RelPicard.RepresentsRelSubPic.nonempty_pullbackAlong_one_iso
Source context 10 commands
Surrounding namespaces, section variables, and local commands at this declaration.
section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.PoincareIdentity
universe u
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.NeronModelInfra
open _root_.GoodReductionJacobian
open _root_.AlgebraicGeometry.RelPicardLean source · statement
theorem _root_.AlgebraicGeometry.RelPicard.RepresentsRelSubPic.nonempty_pullbackAlong_one_iso
{R : Type u} [CommRing R] {C : Scheme.{u}} {c : C ⟶ Spec (CommRingCat.of R)}
{ε : SchemeHomOver (𝟙 (Spec (CommRingCat.of R))) c}
{P : SubPicGroupCondition c ε} {D : RelativePic0Designation R c}
(h : RepresentsRelSubPic c ε P.toSubPicCondition D)
{T : Scheme.{u}} (t : T ⟶ Spec (CommRingCat.of R)) :
Nonempty ((h.poincare.pullbackAlong (h.relativeGroupLaw.one t)).L ≅
(RigidifiedLineBundle.unit (c := c) (ε := ε) t).L)