Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.affineBasisCover
(X : AlgebraicGeometry.Scheme) → X.OpenCover
We may bind the basic open sets of an open affine cover to form an affine cover that is also a basis.
- Defined in
- Mathlib.AlgebraicGeometry.Cover.Open
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 140 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.
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
- CategoryTheory.PreZeroHypercover.I₀proof · cited by 763
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverproof · cited by 469
- AlgebraicGeometry.Scheme.OpenCoverstatement · cited by 207
- AlgebraicGeometry.LocallyRingedSpace.toTopCatproof · cited by 128
- AlgebraicGeometry.Scheme.affineCoverproof · cited by 61
- CategoryTheory.Precoverage.ZeroHypercover.bindproof · cited by 8
- AlgebraicGeometry.Scheme.affineBasisCoverOfAffineproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.isBasis_affineOpensproof · cited by 37
- AlgebraicGeometry.Scheme.affineBasisCover_is_basisstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.affineBasisCoverRingstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.affineBasisCover_map_rangestatement · cited by 1
- AlgebraicGeometry.reduce_to_affine_globalproof · cited by 1
- AlgebraicGeometry.Scheme.affineBasisCover_objstatement and proof · cited by 0