Theorems · Definition · algebraic geometry
AlgebraicGeometry.affineOpensRestrict
{X : AlgebraicGeometry.Scheme} → (U : X.Opens) → ↑(↑U).affineOpens ≃ { V // ↑V ≤ U }The affine open sets of an open subscheme corresponds to the affine open sets containing in the subset.
- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- 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.Scheme.Opens.toSchemestatement · cited by 433
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.sourceAffineLocally_morphismRestrictproof · cited by 2
- AlgebraicGeometry.affineOpensRestrict_apply_coe_coestatement and proof · cited by 0
- AlgebraicGeometry.affineOpensRestrict_symm_apply_coestatement · cited by 0