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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- TopCatstatement · cited by 1,889
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- AlgebraicGeometry.PresheafedSpace.Hom.basestatement and proof · cited by 1,135
Cited by14
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.range_fromSpecResidueFieldproof · cited by 4
- AlgebraicGeometry.Scheme.Pullback.Triplet.snd_SpecTensorTo_applyproof · cited by 2
- AlgebraicGeometry.Scheme.Pullback.Triplet.fst_SpecTensorTo_applyproof · cited by 2
- AlgebraicGeometry.ext_of_apply_eqproof · cited by 1
- AlgebraicGeometry.ext_of_fromSpecResidueField_eqproof · cited by 1
- AlgebraicGeometry.Scheme.exists_fac_of_etale_of_isSepClosedproof · cited by 1
- AlgebraicGeometry.Scheme.pointSmallEtaleFiberObjToPreimage_surjectiveproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.asFiberHom_applyproof · cited by 1
- AlgebraicGeometry.ValuativeCriterion.Existence.specializingMapproof · cited by 1
- AlgebraicGeometry.pointOfClosedPoint_applyproof · cited by 1
- AlgebraicGeometry.isClosed_singleton_iff_locallyOfFiniteTypeproof · cited by 0
- AlgebraicGeometry.Scheme.isConservativeFamilyOfPoints_pointSmallEtale'proof · cited by 0