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Theorems · Definition · algebraic geometry

AlgebraicGeometry.basicOpenIsoSpecAway

{R : CommRingCat} →
  (f : ↑R) → ↑(PrimeSpectrum.basicOpen f) ≅ AlgebraicGeometry.Spec (CommRingCat.of (Localization.Away f))

For f : R, D(f) as an open subscheme of Spec R is isomorphic to Spec R[1/f].

Defined in
Mathlib.AlgebraicGeometry.Restrict
Cited by
7 results in Mathlib
Foundations
Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AlgebraicGeometry.Proj.toBasicOpenOfGlobalSections · cited by 7Proj.toBasicOpenOfGlobalS…AlgebraicGeometry.Proj.fromOfGlobalSections_preimage_basicOpen · cited by 2Proj.fromOfGlobalSections…AlgebraicGeometry.basicOpenIsoSpecAway_hom_SpecMap · cited by 1AlgebraicGeometry.basicOp…AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE · cited by 1AlgebraicGeometry.basicOp…AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE_assoc · cited by 1AlgebraicGeometry.basicOp…AlgebraicGeometry.Proj.fromOfGlobalSections_toSpecZero · cited by 1Proj.fromOfGlobalSections…AlgebraicGeometry.Proj.homOfLE_toBasicOpenOfGlobalSections_ι · cited by 1Proj.homOfLE_toBasicOpenO…AlgebraicGeometry.SpecMapRestrictBasicOpenIso · cited by 1AlgebraicGeometry.SpecMap…AlgebraicGeometry.basicOpenIsoSpecAway_hom_SpecMap_assoc · cited by 0AlgebraicGeometry.basicOp…Algebra.algebraMap · cited by 4706Algebra.algebraMapCategoryTheory.Iso · cited by 3963CategoryTheory.IsoAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatCommRingCat.carrier · cited by 1096CommRingCat.carrierAlgebraicGeometry.Spec · cited by 626AlgebraicGeometry.SpecAlgebraicGeometry.Scheme.Opens.toScheme · cited by 433Opens.toSchemeSubmonoid.powers · cited by 408Submonoid.powersAlgebraicGeometry.Spec.map · cited by 332Spec.mapAlgebraicGeometry.Scheme.Opens.ι · cited by 275Opens.ιCommRingCat.ofHom · cited by 259CommRingCat.ofHomPrimeSpectrum.basicOpen · cited by 163PrimeSpectrum.basicOpenLocalization.Away · cited by 162Localization.AwayAlgebraicGeometry.IsOpenImmersion.isoOfRangeEq · cited by 16IsOpenImmersion.isoOfRang…AlgebraicGeometry.basicOpenIs…CITED BYCITES

Cites14

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Cited by9

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