Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffineOpen.basicOpen
∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens},
AlgebraicGeometry.IsAffineOpen U →
∀ (f : ↑(X.presheaf.obj (Opposite.op U))), AlgebraicGeometry.IsAffineOpen (X.basicOpen f)- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CommRingproof · cited by 17,173
- Oppositestatement · cited by 8,081
- Algebra.algebraMapproof · cited by 4,706
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement and proof · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
Cited by19
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locallyproof · cited by 3
- AlgebraicGeometry.Scheme.exists_le_and_germ_injectiveproof · cited by 3
- AlgebraicGeometry.exists_smooth_of_formallySmooth_stalkproof · cited by 2
- AlgebraicGeometry.affineAnd_isLocalproof · cited by 2
- AlgebraicGeometry.IsAffineOpen.Spec_basicOpenproof · cited by 2
- AlgebraicGeometry.isAffine_of_isAffineOpen_basicOpenproof · cited by 2
- AlgebraicGeometry.isCompact_basicOpenproof · cited by 1
- AlgebraicGeometry.exists_basicOpen_le_appLE_of_appLE_of_isAffineproof · cited by 1
- AlgebraicGeometry.Scheme.exists_isQuasiAffine_of_isLimitproof · cited by 1
- AlgebraicGeometry.sourceAffineLocally_isLocalproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.le_of_iSup_eq_topproof · cited by 1
- AlgebraicGeometry.isBasis_preimage_isAffineOpenproof · cited by 1