Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.fromSpecStalk_closedPoint
∀ {X : AlgebraicGeometry.Scheme} {x : ↥X}, (X.fromSpecStalk x) (IsLocalRing.closedPoint ↑(X.presheaf.stalk x)) = x- Defined in
- Mathlib.AlgebraicGeometry.Stalk
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 148 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 · 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 · cited by 1,135
Cited by7
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.fromSpecResidueField_applyproof · cited by 14
- AlgebraicGeometry.spread_out_of_isGermInjective'proof · cited by 3
- AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec_fromSpecStalkproof · cited by 2
- AlgebraicGeometry.ValuativeCriterion.Existence.specializingMapproof · cited by 1
- AlgebraicGeometry.spread_out_unique_of_isGermInjective'proof · cited by 1
- AlgebraicGeometry.Scheme.range_fromSpecStalkproof · cited by 0