Theorems · Definition · algebraic geometry
AlgebraicGeometry.IsAffineOpen.primeIdealOf
{X : AlgebraicGeometry.Scheme} →
{U : X.Opens} → AlgebraicGeometry.IsAffineOpen U → ↥U → PrimeSpectrum ↑(X.presheaf.obj (Opposite.op U))The prime ideal of 𝒪ₓ(U) corresponding to a point x : U.
- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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 · cited by 19,642
- Oppositestatement · cited by 8,081
- CategoryTheory.Iso.homproof · cited by 7,684
- 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
Cited by16
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsAffineOpen.fromSpec_primeIdealOfstatement · cited by 3
- AlgebraicGeometry.IsAffineOpen.isLocalization_stalkstatement and proof · cited by 3
- AlgebraicGeometry.formallySmooth_stalkMap_iffstatement and proof · cited by 3
- AlgebraicGeometry.exists_smooth_of_formallySmooth_stalkproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.quasiFiniteAtstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_topproof · cited by 1
- AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAtproof · cited by 1
- AlgebraicGeometry.IsAffineOpen.arrowStalkMapIsostatement and proof · cited by 1
- AlgebraicGeometry.IsAffineOpen.primeIdealOf_eq_map_closedPointstatement · cited by 1
- AlgebraicGeometry.IsAffineOpen.primeIdealOf_genericPointstatement · cited by 1
- AlgebraicGeometry.IsAffineOpen.comap_primeIdealOf_appLEstatement · cited by 1