Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Proj.basicOpenToSpec_SpecMap_awayMap_assoc

∀ {σ : Type u_1} {A : Type u} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubgroupClass σ A] (𝒜 : ℕ → σ)
  [inst_3 : GradedRing 𝒜] {f : A} {m' : ℕ} {g : A} (g_deg : g ∈ 𝒜 m') {x : A} (hx : x = f * g)
  {Z : AlgebraicGeometry.Scheme} (h : AlgebraicGeometry.Spec (CommRingCat.of (HomogeneousLocalization.Away 𝒜 f)) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Proj.basicOpenToSpec 𝒜 x)
      (CategoryTheory.CategoryStruct.comp
        (AlgebraicGeometry.Spec.map (CommRingCat.ofHom (HomogeneousLocalization.awayMap 𝒜 g_deg hx))) h) =
    CategoryTheory.CategoryStruct.comp ((AlgebraicGeometry.Proj 𝒜).homOfLE ⋯)
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Proj.basicOpenToSpec 𝒜 f) h)

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic

Cited by

1 results in Mathlib

Foundations

Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing