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Theorems · Definition · algebraic geometry

AlgebraicGeometry.IsAffineOpen.isoSpec

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

The isomorphism U ≅ Spec Γ(X, U) for an affine U.

Defined in
Mathlib.AlgebraicGeometry.AffineScheme
Cited by
48 results in Mathlib
Foundations
Depth 143 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.fromSpec · cited by 65IsAffineOpen.fromSpecAlgebraicGeometry.Scheme.IdealSheafData.glueDataObjι · cited by 20IdealSheafData.glueDataOb…AlgebraicGeometry.IsAffineOpen.primeIdealOf · cited by 15IsAffineOpen.primeIdealOfAlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app · cited by 5IdealSheafData.subschemeι…AlgebraicGeometry.Scheme.Hom.normalizationDesc_comp · cited by 5Hom.normalizationDesc_compAlgebraicGeometry.IsAffineOpen.fromSpec_primeIdealOf · cited by 3IsAffineOpen.fromSpec_pri…AlgebraicGeometry.IsAffineOpen.fromSpec_top · cited by 3IsAffineOpen.fromSpec_topAlgebraicGeometry.IsAffineOpen.isoSpec_hom · cited by 3IsAffineOpen.isoSpec_homAlgebraicGeometry.IsAffineOpen.isoSpec_inv_appTop · cited by 3IsAffineOpen.isoSpec_inv_…AlgebraicGeometry.IsAffineOpen.isoSpec_inv_ι · cited by 3IsAffineOpen.isoSpec_inv_ιAlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv · cited by 3IsAffineOpen.toSpecΓ_isoS…AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_ι · cited by 3IdealSheafData.glueDataOb…AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec · cited by 2AffineZariskiSite.restric…AlgebraicGeometry.isIso_pushoutSection_of_isAffineOpen · cited by 2AlgebraicGeometry.isIso_p…AlgebraicGeometry.IsLocallyArtinian.of_topologicalKrullDim_le_zero · cited by 2IsLocallyArtinian.of_topo…CategoryTheory.Functor.obj · cited by 19642Functor.objOpposite · cited by 8081OppositeCategoryTheory.Iso · cited by 3963CategoryTheory.IsoTopCat.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.presheafCategoryTheory.Iso.symm · cited by 993Iso.symmAlgebraicGeometry.Spec · cited by 626AlgebraicGeometry.SpecIsAffineOpen.isoSpecCITED BYCITES

Cites23

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Cited by53

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