Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.AffineOpenCover
AlgebraicGeometry.Scheme → Type (max (v + 1) (u + 1))
An affine open cover of X consists of a family of open immersions into X from
spectra of rings.
- Defined in
- Mathlib.AlgebraicGeometry.Cover.Open
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.IsOpenImmersionproof · cited by 476
- AlgebraicGeometry.Scheme.AffineCoverproof · cited by 10
Cited by13
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.AffineOpenCover.openCoverstatement and proof · cited by 17
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeCoverstatement · cited by 10
- AlgebraicGeometry.Scheme.affineOpenCoverstatement · cited by 8
- AlgebraicGeometry.Scheme.AffineOpenCover.openCover_fstatement and proof · cited by 5
- AlgebraicGeometry.Scheme.affineOpenCoverOfSpanRangeEqTopstatement · cited by 5
- AlgebraicGeometry.Scheme.OpenCover.affineRefinementstatement · cited by 5
- AlgebraicGeometry.Scheme.AffineOpenCover.ofIsOpenCoverstatement · cited by 4
- AlgebraicGeometry.Proj.affineOpenCoverstatement · cited by 4
- AlgebraicGeometry.Proj.mapAffineOpenCoverstatement · cited by 3
- AlgebraicGeometry.Scheme.AffineOpenCover.openCover_I₀statement and proof · cited by 0
- AlgebraicGeometry.Scheme.AffineOpenCover.openCover_Xstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Modules.exists_affineOpenCover_presentationstatement · cited by 0