Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Modules.restrictUnitIso

{X Y : AlgebraicGeometry.Scheme} →
  (f : X ⟶ Y) →
    [inst : AlgebraicGeometry.IsOpenImmersion f] →
      AlgebraicGeometry.Scheme.Modules.restrict (SheafOfModules.unit Y.ringCatSheaf) f ≅
        SheafOfModules.unit X.ringCatSheaf

Scheme.Modules.restrict along an open immersion X ⟶ Y sends 𝒪_Y to 𝒪_X.

Defined in: Mathlib.AlgebraicGeometry.Modules.Sheaf
Cited by: 1 results in Mathlib
Foundations: Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.IsOpenImmersion

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Cites28

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Quiver.Homstatement and proof · cited by 32,603
Oppositeproof · cited by 8,081
CategoryTheory.Functor.compproof · cited by 6,529
CategoryTheory.Isostatement · cited by 3,963
TopCat.carrierstatement and proof · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CommRingCatstatement and proof · cited by 2,333
Opposite.unopproof · cited by 2,231
TopologicalSpace.Opensstatement and proof · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892

Cited by2

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Modules.presentationRestrictproof · cited by 1
AlgebraicGeometry.Scheme.Modules.exists_isOpenCover_presentationproof · cited by 1