Theorems · Theorem · algebraic geometry

ProjectiveSpectrum.mem_vanishingIdeal

∀ {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)) (f : A),
  f ∈ ProjectiveSpectrum.vanishingIdeal t ↔ ∀ x ∈ t, f ∈ x.asHomogeneousIdeal

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology

Cited by

2 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubmonoidClassGradedRing