Theorems · Theorem · algebraic geometry

ProjectiveSpectrum.vanishingIdeal_closure

∀ {A : Type u_1} {σ : Type u_2} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubmonoidClass σ A] (𝒜 : ℕ → σ)
  [inst_3 : GradedRing 𝒜] (t : Set (ProjectiveSpectrum 𝒜)),
  ProjectiveSpectrum.vanishingIdeal (closure t) = ProjectiveSpectrum.vanishingIdeal t

Defined in: Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology
Cited by: 0 results in Mathlib
Foundations: Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing SetLike AddSubmonoidClass GradedRing

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites16

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
CommRingstatement and proof · cited by 17,173
SetLike.coeproof · cited by 8,199
closurestatement · cited by 1,254
SetLikestatement and proof · cited by 1,084
GradedRingstatement and proof · cited by 424
AddSubmonoidClassstatement and proof · cited by 346
HomogeneousIdealstatement · cited by 115
HomogeneousIdeal.toIdealproof · cited by 105
ProjectiveSpectrumstatement and proof · cited by 86
ProjectiveSpectrum.zeroLocusproof · cited by 42
ProjectiveSpectrum.vanishingIdealstatement and proof · cited by 20

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.