Module

OModulePresheaf_isCoherent_coker.lean

Nyll.SchemeTheory.Cohomology.Sheaves.OModulePresheaf_isCoherent_coker
2 declarations indexed from sourceView source ↗

Coherence of the cokernel of a morphism of module presheaves.

Imports4
Imported by2

Declarations

AlgebraicCurves.Cohomology.Sheaves.Proofs.OModulePresheaf_isCoherent_coker.AlgebraicGeometry.OModulePresheaf.G4T.isCoherent_coker
Source context 18 commands

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

section ProofImplementation
namespace AlgebraicCurves.Cohomology.Sheaves.Proofs.OModulePresheaf_isCoherent_coker
open _root_.AlgebraicGeometry
open _root_.CategoryTheory
open _root_.TopologicalSpace
open _root_.Opposite
noncomputable section
namespace AlgebraicGeometry
open _root_.AlgebraicGeometry
namespace OModulePresheaf
open _root_.AlgebraicGeometry.OModulePresheaf
namespace G4T
open _root_.AlgebraicGeometry.OModulePresheaf
open _root_.AlgebraicGeometry
universe u
section PModAlg
variable {R : Type u} [CommRing R] {V : Scheme.{u}} {π : V ⟶ Spec (.of R)}
variable {F G : OModulePresheaf π} (φ : OModulePresheaf.Hom F G)
theorem isCoherent_coker (hG : OModulePresheaf.IsCoherent G) :
    OModulePresheaf.IsCoherent (OModulePresheaf.coker φ)
AlgebraicGeometry.OModulePresheaf.isCoherent_coker
Source context 9 commands

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

section ProofImplementation
namespace AlgebraicCurves.Cohomology.Sheaves.Proofs.OModulePresheaf_isCoherent_coker
open _root_.AlgebraicGeometry
open _root_.CategoryTheory
open _root_.TopologicalSpace
open _root_.Opposite
universe u
open _root_.AlgebraicCurves.Cohomology.Sheaves.Proofs in
open _root_.AlgebraicGeometry OModulePresheaf_isCoherent_coker.AlgebraicGeometry in
theorem _root_.AlgebraicGeometry.OModulePresheaf.isCoherent_coker {R : Type u} [CommRing R] {V :
    Scheme.{u}} {π : V ⟶ Spec (.of R)} {F G : OModulePresheaf π} (φ : OModulePresheaf.Hom F G) (hG
    : G.IsCoherent) : (OModulePresheaf.coker φ).IsCoherent