Theorems · Theorem · algebraic geometry

AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_germ

∀ {A : Type u_1} {σ : Type u_2} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubgroupClass σ A] (𝒜 : ℕ → σ)
  [inst_3 : GradedRing 𝒜] (f : A) (x : ↑(ProjectiveSpectrum.top 𝒜)) (hx : x ∈ ProjectiveSpectrum.basicOpen 𝒜 f),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection 𝒜 f)
      ((AlgebraicGeometry.ProjectiveSpectrum.Proj.structureSheaf 𝒜).presheaf.germ (ProjectiveSpectrum.basicOpen 𝒜 f) x
        hx) =
    CategoryTheory.CategoryStruct.comp (CommRingCat.ofHom (HomogeneousLocalization.mapId 𝒜 ⋯))
      (AlgebraicGeometry.Proj.stalkIso' 𝒜 x).toCommRingCatIso.inv

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme

Cited by

1 results in Mathlib

Foundations

Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing