Theorems · Theorem · algebraic geometry

AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_fromSpec

∀ {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} {m : ℕ} (f_deg : f ∈ 𝒜 m) (hm : 0 < m)
  (x :
    ↑↑(AlgebraicGeometry.Spec.locallyRingedSpaceObj
            (CommRingCat.of (HomogeneousLocalization.Away 𝒜 f))).toPresheafedSpace),
  (CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec 𝒜 f))
      (AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.toFun f_deg hm x) =
    x

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme

Cited by

1 results in Mathlib

Foundations

Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing