Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.affineOpens
(X : AlgebraicGeometry.Scheme) → Set X.Opens
The set of affine opens as a subset of opens X.
- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 220 results in Mathlib
- Foundations
- Depth 138 from the axioms, rests on 5,517 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.ofPredproof · cited by 6,101
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
- AlgebraicGeometry.IsAffineOpenproof · cited by 222
Cited by257
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IdealSheafData.idealstatement · cited by 88
- AlgebraicGeometry.Scheme.Hom.kerproof · cited by 51
- AlgebraicGeometry.Scheme.isBasis_affineOpensstatement · cited by 37
- AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjstatement and proof · cited by 24
- AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjιstatement and proof · cited by 20
- AlgebraicGeometry.Scheme.affineBasicOpenstatement and proof · cited by 19
- AlgebraicGeometry.Scheme.IdealSheafData.extstatement and proof · cited by 16
- AlgebraicGeometry.Scheme.Hom.ker_applystatement and proof · cited by 14
- AlgebraicGeometry.iSup_affineOpens_eq_topstatement and proof · cited by 13
- AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdealproof · cited by 13
- AlgebraicGeometry.targetAffineLocallyproof · cited by 12
- AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHomstatement and proof · cited by 10
Showing the 200 most cited of 257.