Theorems · Theorem · algebraic geometry

AlgebraicGeometry.ProjectiveSpectrum.comapFun_asHomogeneousIdeal

∀ {A : Type u_1} {B : Type u_2} {σ : Type u_4} {τ : Type u_5} [inst : CommRing A] [inst_1 : SetLike σ A]
  [inst_2 : AddSubgroupClass σ A] [inst_3 : CommRing B] [inst_4 : SetLike τ B] [inst_5 : AddSubgroupClass τ B]
  {𝒜 : ℕ → σ} {ℬ : ℕ → τ} [inst_6 : GradedRing 𝒜] [inst_7 : GradedRing ℬ] (f : 𝒜 →+*ᵍ ℬ)
  (hf : HomogeneousIdeal.irrelevant ℬ ≤ HomogeneousIdeal.map f (HomogeneousIdeal.irrelevant 𝒜))
  (p : ProjectiveSpectrum ℬ),
  (AlgebraicGeometry.ProjectiveSpectrum.comapFun f hf p).asHomogeneousIdeal =
    HomogeneousIdeal.comap f p.asHomogeneousIdeal

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Functor

Cited by

0 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassCommRingSetLikeAddSubgroupClassGradedRingGradedRing