Theorems · Theorem · algebraic geometry

ProjectiveSpectrum.subset_zeroLocus_iff_subset_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)) (s : Set A),
  t ⊆ ProjectiveSpectrum.zeroLocus 𝒜 s ↔ s ⊆ ↑(ProjectiveSpectrum.vanishingIdeal t)

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology

Cited by

1 results in Mathlib

Foundations

Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubmonoidClassGradedRing