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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.fromSpecResidueField_apply

∀ {X : AlgebraicGeometry.Scheme} (x : ↥X) (s : ↥(AlgebraicGeometry.Spec (X.residueField x))),
  (X.fromSpecResidueField x) s = x
Defined in
Mathlib.AlgebraicGeometry.ResidueField
Cited by
14 results in Mathlib
Foundations
Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

AlgebraicGeometry.Scheme.range_fromSpecResidueField · cited by 4Scheme.range_fromSpecResi…AlgebraicGeometry.Scheme.Pullback.Triplet.snd_SpecTensorTo_apply · cited by 2Triplet.snd_SpecTensorTo_…AlgebraicGeometry.Scheme.Pullback.Triplet.fst_SpecTensorTo_apply · cited by 2Triplet.fst_SpecTensorTo_…AlgebraicGeometry.ext_of_apply_eq · cited by 1AlgebraicGeometry.ext_of_…AlgebraicGeometry.ext_of_fromSpecResidueField_eq · cited by 1AlgebraicGeometry.ext_of_…AlgebraicGeometry.Scheme.exists_fac_of_etale_of_isSepClosed · cited by 1Scheme.exists_fac_of_etal…AlgebraicGeometry.Scheme.pointSmallEtaleFiberObjToPreimage_surjective · cited by 1Scheme.pointSmallEtaleFib…AlgebraicGeometry.Scheme.Hom.asFiberHom_apply · cited by 1Hom.asFiberHom_applyAlgebraicGeometry.ValuativeCriterion.Existence.specializingMap · cited by 1Existence.specializingMapAlgebraicGeometry.pointOfClosedPoint_apply · cited by 1AlgebraicGeometry.pointOf…AlgebraicGeometry.isClosed_singleton_iff_locallyOfFiniteType · cited by 0AlgebraicGeometry.isClose…AlgebraicGeometry.Scheme.isConservativeFamilyOfPoints_pointSmallEtale' · cited by 0Scheme.isConservativeFami…AlgebraicGeometry.Scheme.Pullback.SpecTensorTo_SpecOfPoint · cited by 0Pullback.SpecTensorTo_Spe…AlgebraicGeometry.tfae_universallyInjective · cited by 0AlgebraicGeometry.tfae_un…DFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeContinuousMap · cited by 2491ContinuousMapCommRingCat · cited by 2333CommRingCatAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…TopCat · cited by 1889TopCatAlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.PresheafedSpace.Hom.base · cited by 1135Hom.baseAlgebraicGeometry.LocallyRingedSpace.Hom.toHom · cited by 995Hom.toHomAlgebraicGeometry.Scheme.Hom.toLRSHom' · cited by 895Hom.toLRSHom'AlgebraicGeometry.Spec · cited by 626AlgebraicGeometry.SpecScheme.fromSpecResidueField_a…CITED BYCITES

Cites21

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Cited by14

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