Theorems · Theorem · algebraic geometry

AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_specStalkEquiv

∀ {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.basicOpen 𝒜 f)) {m : ℕ} (f_deg : f ∈ 𝒜 m) (hm : 0 < m),
  CategoryTheory.CategoryStruct.comp
      (AlgebraicGeometry.StructureSheaf.toStalk (HomogeneousLocalization.Away 𝒜 f)
        ((CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec 𝒜 f).base) x))
      (AlgebraicGeometry.ProjectiveSpectrum.Proj.specStalkEquiv 𝒜 f x f_deg hm).hom =
    CommRingCat.ofHom (HomogeneousLocalization.mapId 𝒜 ⋯)

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme

Cited by

1 results in Mathlib

Foundations

Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing