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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.affineOpens

(X : AlgebraicGeometry.Scheme) → Set X.Opens

The set of affine opens as a subset of opens X.

Defined in
Mathlib.AlgebraicGeometry.AffineScheme
Cited by
220 results in Mathlib
Foundations
Depth 138 from the axioms, rests on 5,517 definitions · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.Scheme.IdealSheafData.ideal · cited by 88IdealSheafData.idealAlgebraicGeometry.Scheme.Hom.ker · cited by 51Hom.kerAlgebraicGeometry.Scheme.isBasis_affineOpens · cited by 37Scheme.isBasis_affineOpensAlgebraicGeometry.Scheme.IdealSheafData.glueDataObj · cited by 24IdealSheafData.glueDataObjAlgebraicGeometry.Scheme.IdealSheafData.glueDataObjι · cited by 20IdealSheafData.glueDataOb…AlgebraicGeometry.Scheme.affineBasicOpen · cited by 19Scheme.affineBasicOpenAlgebraicGeometry.Scheme.IdealSheafData.ext · cited by 16IdealSheafData.extAlgebraicGeometry.Scheme.Hom.ker_apply · cited by 14Hom.ker_applyAlgebraicGeometry.iSup_affineOpens_eq_top · cited by 13AlgebraicGeometry.iSup_af…AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal · cited by 13IdealSheafData.vanishingI…AlgebraicGeometry.targetAffineLocally · cited by 12AlgebraicGeometry.targetA…AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom · cited by 10IdealSheafData.glueDataOb…AlgebraicGeometry.Scheme.IdealSheafData.radical · cited by 10IdealSheafData.radicalAlgebraicGeometry.Scheme.IdealSheafData.subschemeCover · cited by 10IdealSheafData.subschemeC…AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk · cited by 8Scheme.SpecMap_stalkMap_f…Set · cited by 53352SetSet.ofPred · cited by 6101Set.ofPredAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.Scheme.Opens · cited by 1149Scheme.OpensAlgebraicGeometry.IsAffineOpen · cited by 222AlgebraicGeometry.IsAffin…Scheme.affineOpensCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by257

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 257.