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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Spec.locallyRingedSpaceObj

CommRingCat → AlgebraicGeometry.LocallyRingedSpace

The spectrum of a commutative ring, as a LocallyRingedSpace.

Defined in
Mathlib.AlgebraicGeometry.Spec
Cited by
57 results in Mathlib
Foundations
Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

AlgebraicGeometry.Spec · cited by 626AlgebraicGeometry.SpecAlgebraicGeometry.Spec.toLocallyRingedSpace · cited by 30Spec.toLocallyRingedSpaceAlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec · cited by 13Proj.toSpecAlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier · cited by 9FromSpec.carrierAlgebraicGeometry.ProjIsoSpecTopComponent.toSpec · cited by 9ProjIsoSpecTopComponent.t…AlgebraicGeometry.Spec.locallyRingedSpaceMap · cited by 7Spec.locallyRingedSpaceMapAlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdeal · cited by 4carrier.asIdealAlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.toFun · cited by 4FromSpec.toFunAlgebraicGeometry.LocallyRingedSpace.toΓSpec · cited by 4LocallyRingedSpace.toΓSpecAlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.toFun · cited by 3ToSpec.toFunAlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq · cited by 3Proj.toSpec_base_apply_eqAlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.denom_notMem · cited by 2carrier.denom_notMemAlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.zero_mem · cited by 2carrier.zero_memAlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff_of_mem · cited by 2FromSpec.mem_carrier_iff_…AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.preimage_basicOpen · cited by 2ToSpec.preimage_basicOpenCommRingCat · cited by 2333CommRingCatAlgebraicGeometry.LocallyRingedSpace · cited by 205AlgebraicGeometry.Locally…AlgebraicGeometry.SheafedSpace · cited by 142AlgebraicGeometry.Sheafed…AlgebraicGeometry.Spec.sheafedSpaceObj · cited by 24Spec.sheafedSpaceObjSpec.locallyRingedSpaceObjCITED BYCITES

Cites4

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

Cited by72

Results whose statement or proof uses this declaration.