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Theorems · Definition · algebraic geometry

AlgebraicGeometry.IsAffineOpen.fromSpec

{X : AlgebraicGeometry.Scheme} →
  {U : X.Opens} → AlgebraicGeometry.IsAffineOpen U → (AlgebraicGeometry.Spec (X.presheaf.obj (Opposite.op U)) ⟶ X)

The open immersion Spec Γ(X, U) ⟶ X for an affine U.

Defined in
Mathlib.AlgebraicGeometry.AffineScheme
Cited by
65 results in Mathlib
Foundations
Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

AlgebraicGeometry.IsAffineOpen.basicOpen · cited by 19IsAffineOpen.basicOpenAlgebraicGeometry.IsAffineOpen.isLocalization_basicOpen · cited by 18IsAffineOpen.isLocalizati…AlgebraicGeometry.IsAffineOpen.isCompact · cited by 17IsAffineOpen.isCompactAlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal · cited by 13IdealSheafData.vanishingI…AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_self · cited by 10IsAffineOpen.fromSpec_pre…AlgebraicGeometry.Scheme.Hom.normalizationDesc · cited by 10Hom.normalizationDescAlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk · cited by 8Scheme.SpecMap_stalkMap_f…AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpec · cited by 8IsAffineOpen.SpecMap_appL…AlgebraicGeometry.IsAffineOpen.range_fromSpec · cited by 8IsAffineOpen.range_fromSp…AlgebraicGeometry.Scheme.SpecMap_stalkSpecializes_fromSpecStalk · cited by 6Scheme.SpecMap_stalkSpeci…AlgebraicGeometry.IsAffineOpen.fromSpec_app_self · cited by 6IsAffineOpen.fromSpec_app…AlgebraicGeometry.Scheme.Hom.toNormalization_fromNormalization · cited by 6Hom.toNormalization_fromN…AlgebraicGeometry.IsAffineOpen.toSpecΓ_fromSpec · cited by 6IsAffineOpen.toSpecΓ_from…AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app · cited by 5IdealSheafData.subschemeι…AlgebraicGeometry.IsAffineOpen.fromSpecStalk · cited by 5IsAffineOpen.fromSpecStalkQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compOpposite · cited by 8081OppositeCategoryTheory.Iso.inv · cited by 6514Iso.invTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.Scheme.Opens · cited by 1149Scheme.OpensAlgebraicGeometry.PresheafedSpace.presheaf · cited by 1104PresheafedSpace.presheafIsAffineOpen.fromSpecCITED BYCITES

Cites19

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Cited by71

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