Theorems · Theorem · algebraic geometry

ProjectiveSpectrum.gc_ideal

∀ {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],
  GaloisConnection (fun I => ProjectiveSpectrum.zeroLocus 𝒜 ↑I) fun t => (ProjectiveSpectrum.vanishingIdeal t).toIdeal

zeroLocus and vanishingIdeal form a Galois connection.

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology

Cited by

12 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubmonoidClassGradedRing