Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.affineCover
(X : AlgebraicGeometry.Scheme) → X.OpenCover
The affine cover of a scheme.
- Defined in
- Mathlib.AlgebraicGeometry.Cover.Open
- Cited by
- 61 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Isoproof · cited by 3,963
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatproof · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierproof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
- AlgebraicGeometry.Specproof · cited by 626
Cited by68
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsZariskiLocalAtSource.compproof · cited by 10
- AlgebraicGeometry.Scheme.affineOpenCoverproof · cited by 8
- AlgebraicGeometry.IsZariskiLocalAtTarget.of_isPullbackproof · cited by 6
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- AlgebraicGeometry.Scheme.affineBasisCoverproof · cited by 5
- AlgebraicGeometry.Scheme.OpenCover.affineRefinementproof · cited by 5
- AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIsostatement and proof · cited by 4
- AlgebraicGeometry.HasAffineProperty.isStableUnderBaseChangeproof · cited by 3
- AlgebraicGeometry.compactSpace_iff_existsproof · cited by 2
- AlgebraicGeometry.IsIntegralHom.iff_universallyClosed_and_isAffineHomproof · cited by 2
- AlgebraicGeometry.LocallyOfFiniteType.isLocallyNoetherianproof · cited by 2
- AlgebraicGeometry.LocallyOfFiniteType.jacobsonSpaceproof · cited by 2