Theorems · Definition · algebraic geometry
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toScheme
{X : AlgebraicGeometry.PresheafedSpace CommRingCat} →
(Y : AlgebraicGeometry.Scheme) →
(f : X ⟶ Y.toPresheafedSpace) → [H : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f] → AlgebraicGeometry.SchemeIf X ⟶ Y is an open immersion, and Y is a scheme, then so is X.
- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement and proof · cited by 2,333
- 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
- AlgebraicGeometry.PresheafedSpacestatement and proof · cited by 260
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersionstatement and proof · cited by 44
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toLocallyRingedSpaceproof · cited by 5
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.schemeproof · cited by 0
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.restrictproof · cited by 10
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toSchemeHomstatement · cited by 1
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toSchemeHom_toPshHomstatement · cited by 0
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toScheme_toLocallyRingedSpacestatement · cited by 0
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.scheme_toSchemestatement · cited by 0
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toScheme.congr_simpstatement and proof · cited by 0