Theorems · Definition · algebraic geometry

AlgebraicGeometry.projIsoSpec

{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 ∈ 𝒜 m →
                    0 < m →
                      ((AlgebraicGeometry.Proj.toLocallyRingedSpace 𝒜).restrict ⋯ ≅
                        AlgebraicGeometry.Spec.locallyRingedSpaceObj
                          (CommRingCat.of (HomogeneousLocalization.Away 𝒜 f)))

If f ∈ A is a homogeneous element of positive degree, then the projective spectrum restricted to D(f) as a locally ringed space is isomorphic to Spec A⁰_f.

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme

Cited by

0 results in Mathlib

Foundations

Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing