Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffineOpen.inf
∀ {X : AlgebraicGeometry.Scheme}
[AlgebraicGeometry.IsAffineHom (CategoryTheory.Limits.pullback.diagonal (CategoryTheory.Limits.terminal.from X))]
{U V : X.Opens},
AlgebraicGeometry.IsAffineOpen U → AlgebraicGeometry.IsAffineOpen V → AlgebraicGeometry.IsAffineOpen (U ⊓ V)If X ⟶ Spec ℤ has affine diagonal (in particular when X is separated), then intersections
of affine opens of X are also affine.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
- AlgebraicGeometry.IsAffineOpenstatement and proof · cited by 222
- CategoryTheory.Limits.terminalstatement and proof · cited by 141
- CategoryTheory.Limits.pullback.diagonalObjstatement · cited by 80
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsAffineOpen.iInfproof · cited by 0
- AlgebraicGeometry.IsAffineOpen.biInfproof · cited by 0