Theorems · Theorem · algebraic geometry
AlgebraicGeometry.stalkClosedPointIso_inv
∀ (R : CommRingCat) [inst : IsLocalRing ↑R],
(AlgebraicGeometry.stalkClosedPointIso R).inv =
AlgebraicGeometry.StructureSheaf.toStalk (↑R) (IsLocalRing.closedPoint ↑R)- Defined in
- Mathlib.AlgebraicGeometry.Stalk
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsLocalRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Iso.invstatement · cited by 6,514
- CommRingCatstatement and proof · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- AlgebraicGeometry.PresheafedSpace.presheafstatement · cited by 1,104
- CommRingCat.carrierstatement and proof · cited by 1,096
- AlgebraicGeometry.Specstatement · cited by 626
- TopCat.Presheaf.stalkstatement · cited by 407
- IsLocalRingstatement and proof · cited by 339
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ΓSpecIso_hom_stalkClosedPointIso_invproof · cited by 2
- AlgebraicGeometry.Spec_stalkClosedPointIsoproof · cited by 1
- AlgebraicGeometry.ValuativeCriterion.Existence.of_specializingMapproof · cited by 1