Theorems · Theorem · algebraic geometry

AlgebraicGeometry.ProjectiveSpectrum.Proj.stalkMap_toSpec

∀ {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),
  AlgebraicGeometry.LocallyRingedSpace.Hom.stalkMap (AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec 𝒜 f) x =
    CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.ProjectiveSpectrum.Proj.specStalkEquiv 𝒜 f x f_deg hm).hom
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Proj.stalkIso' 𝒜 ↑x).toCommRingCatIso.inv
        ((AlgebraicGeometry.Proj.toLocallyRingedSpace 𝒜).restrictStalkIso ⋯ x).inv)

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme

Cited by

1 results in Mathlib

Foundations

Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing