Theorems · Definition · algebraic geometry

AlgebraicGeometry.Proj.basicOpenToSpec

{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) →
                ↑(AlgebraicGeometry.Proj.basicOpen 𝒜 f) ⟶
                  AlgebraicGeometry.Spec (CommRingCat.of (HomogeneousLocalization.Away 𝒜 f))

The canonical map Proj A |_ D₊(f) ⟶ Spec (A_f)₀. This is an isomorphism when f is homogeneous of positive degree. See basicOpenIsoSpec below.

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic

Cited by

5 results in Mathlib

Foundations

Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing