Theorems · Theorem · algebraic geometry
AlgebraicGeometry.ProjectiveSpectrum.Proj.mk_mem_toSpec_base_apply
∀ {A : Type u_1} {σ : Type u_2} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubgroupClass σ A] (𝒜 : ℕ → σ)
[inst_3 : GradedRing 𝒜] {f : A} (x : ↑((AlgebraicGeometry.Proj.toLocallyRingedSpace 𝒜).restrict ⋯).toTopCat)
(z : HomogeneousLocalization.NumDenSameDeg 𝒜 (Submonoid.powers f)),
HomogeneousLocalization.mk z ∈
((CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec 𝒜 f).base) x).asIdeal ↔
↑z.num ∈ (↑x).asHomogeneousIdeal- Cited by
- 1 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
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.Functor.objstatement · cited by 19,642
- CommRingstatement and proof · cited by 17,173
- Idealstatement · cited by 4,748
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ProjectiveSpectrum.Proj.isLocalization_atPrimeproof · cited by 0