Module

Nonempty_thetaBundle_baseChange_iso_thetaBundle_toR.lean

Nyll.JacobianVarieties.Picard.Nonempty_thetaBundle_baseChange_iso_thetaBundle_toR

2 declarations indexed from sourceView source ↗

Module documentation

Transport of theta bundles under base change

The section-twist and pushforward comparison isomorphisms identify Picard bundles under base change. Exterior powers and duality then identify the associated theta bundles.

Imports10

Imported by2

def

dualIso

L82 ↗

JacobianVarieties.Picard.Proofs.Nonempty_thetaBundle_baseChange_iso_thetaBundle_toR.ThetaKSketch.dualIso

Documentation

Dualizing a module isomorphism gives an isomorphism of the dual modules.

Source context 17 commands

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

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.Nonempty_thetaBundle_baseChange_iso_thetaBundle_toR
attribute [-instance]
  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
attribute [-simp]
  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 _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.AlgebraicGeometry
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry.SmoothProperCurve
open _root_.AlgebraicGeometry.RelPicard.BaseChange
namespace ThetaKSketch

Lean source · statement

def dualIso {X : Scheme.{u}} {L L' : X.Modules} (e : L ≅ L') :
    Scheme.Modules.dual L ≅ Scheme.Modules.dual L'

theorem