Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Proj.fromOfGlobalSections_toSpecZero_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] {X : AlgebraicGeometry.Scheme} (f : A →+* ↑(X.presheaf.obj (Opposite.op ⊤)))
  (hf : Ideal.map f (HomogeneousIdeal.irrelevant 𝒜).toIdeal = ⊤) {Z : AlgebraicGeometry.Scheme}
  (h : AlgebraicGeometry.Spec (CommRingCat.of ↥(𝒜 0)) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Proj.fromOfGlobalSections 𝒜 f hf)
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Proj.toSpecZero 𝒜) h) =
    CategoryTheory.CategoryStruct.comp X.toSpecΓ
      (CategoryTheory.CategoryStruct.comp
        (AlgebraicGeometry.Spec.map (CommRingCat.ofHom (f.comp (algebraMap (↥(𝒜 0)) A)))) h)

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic

Cited by

0 results in Mathlib

Foundations

Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing