Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffineOpen.isLocalization_stalk
∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens} (hU : AlgebraicGeometry.IsAffineOpen U) (x : ↥U),
IsLocalization.AtPrime (↑(X.presheaf.stalk ↑x)) (hU.primeIdealOf x).asIdeal- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Oppositestatement · cited by 8,081
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- 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
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.quasiFiniteAtproof · cited by 1
- AlgebraicGeometry.functionField_isFractionRing_of_isAffineOpenproof · cited by 0