Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Proj.mapAffineOpenCover_f

∀ {A B σ τ : Type u} [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))
  (i : (AlgebraicGeometry.Proj.affineOpenCover 𝒜).I₀),
  (AlgebraicGeometry.Proj.mapAffineOpenCover f hf).f i = AlgebraicGeometry.Proj.awayι ℬ (f ↑i.snd) ⋯ ⋯

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Functor

Cited by

1 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassCommRingSetLikeAddSubgroupClassGradedRingGradedRing