Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Proj.basicOpenToSpec_app_top

∀ {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),
  AlgebraicGeometry.Scheme.Hom.app (AlgebraicGeometry.Proj.basicOpenToSpec 𝒜 f) ⊤ =
    CategoryTheory.CategoryStruct.comp
      (AlgebraicGeometry.Scheme.ΓSpecIso (CommRingCat.of (HomogeneousLocalization.Away 𝒜 f))).hom
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Proj.awayToSection 𝒜 f)
        (AlgebraicGeometry.Proj.basicOpen 𝒜 f).topIso.inv)

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic

Cited by

1 results in Mathlib

Foundations

Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing