Theorems · Definition · algebraic geometry
AlgebraicGeometry.stalkClosedPointIso
(R : CommRingCat) → [inst : IsLocalRing ↑R] → (AlgebraicGeometry.Spec R).presheaf.stalk (IsLocalRing.closedPoint ↑R) ≅ R
For a local ring (R, 𝔪),
this is the isomorphism between the stalk of Spec R at 𝔪 and R.
- Defined in
- Mathlib.AlgebraicGeometry.Stalk
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 130 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Isostatement · cited by 3,963
- 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
- CategoryTheory.Iso.symmproof · cited by 993
- AlgebraicGeometry.Specstatement · cited by 626
- CategoryTheory.Iso.transproof · cited by 566
- Ideal.primeComplproof · cited by 462
Cited by10
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.stalkClosedPointToproof · cited by 17
- AlgebraicGeometry.Scheme.germ_stalkClosedPointToproof · cited by 4
- AlgebraicGeometry.stalkClosedPointIso_invstatement · cited by 3
- AlgebraicGeometry.germ_stalkClosedPointIso_homstatement and proof · cited by 2
- AlgebraicGeometry.ΓSpecIso_hom_stalkClosedPointIso_invstatement · cited by 2
- AlgebraicGeometry.Scheme.stalkClosedPointTo_compproof · cited by 1
- AlgebraicGeometry.Spec_stalkClosedPointIsostatement · cited by 1
- AlgebraicGeometry.ValuativeCriterion.Existence.of_specializingMapproof · cited by 1
- AlgebraicGeometry.germ_stalkClosedPointIso_hom_assocstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Specproof · cited by 0