Theorems · Theorem · algebraic geometry

AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply

∀ {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 : ↑(CommRingCat.of (HomogeneousLocalization.Away 𝒜 f)))
  (p : ↥(Opposite.unop (Opposite.op (ProjectiveSpectrum.basicOpen 𝒜 f)))),
  HomogeneousLocalization.val (↑((AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection 𝒜 f).hom' x) p) =
    (IsLocalization.map (Localization (↑p).asHomogeneousIdeal.toIdeal.primeCompl) (RingHom.id A) ⋯)
      (HomogeneousLocalization.val x)

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommRingSetLikeAddSubgroupClassGradedRing