Theorems · Theorem · algebraic geometry

AlgebraicGeometry.germ_comp_stalkToFiberRingHom

∀ {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] (U : TopologicalSpace.Opens ↑(ProjectiveSpectrum.top 𝒜)) (x : ↑(ProjectiveSpectrum.top 𝒜))
  (hx : x ∈ U),
  CategoryTheory.CategoryStruct.comp ((AlgebraicGeometry.ProjectiveSpectrum.Proj.structureSheaf 𝒜).presheaf.germ U x hx)
      (AlgebraicGeometry.stalkToFiberRingHom 𝒜 x) =
    AlgebraicGeometry.openToLocalization 𝒜 U x hx

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf

Cited by

1 results in Mathlib

Foundations

Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing