Theorems · Definition · algebraic geometry

AlgebraicGeometry.Proj.basicOpenIsoSpec

{σ : Type u_1} →
  {A : Type u} →
    [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 ∈ 𝒜 m →
                    0 < m →
                      (↑(AlgebraicGeometry.Proj.basicOpen 𝒜 f) ≅
                        AlgebraicGeometry.Spec (CommRingCat.of (HomogeneousLocalization.Away 𝒜 f)))

The canonical isomorphism Proj A |_ D₊(f) ≅ Spec (A_f)₀ when f is homogeneous of positive degree.

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic

Cited by

11 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing