AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine

{X : AlgebraicGeometry.Scheme} →
  [AlgebraicGeometry.IsAffine X] → X.IdealSheafData ≃+*o Ideal ↑(X.presheaf.obj (Opposite.op ⊤))

Over affine schemes, ideal sheaves are in bijection with ideals of the global sections.

Defined in: Mathlib.AlgebraicGeometry.IdealSheaf.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.IsAffine

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

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

CategoryTheory.Functor.objstatement and proof · cited by 19,642
Top.topstatement and proof · cited by 9,680
Oppositestatement · cited by 8,081
Idealstatement and proof · cited by 4,748
TopCat.carrierstatement · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CommRingCatstatement · cited by 2,333
TopologicalSpace.Opensstatement · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734

Results whose statement or proof uses this declaration.