Theorems · Definition · algebraic geometry

AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec

{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) →
                (AlgebraicGeometry.Proj.toLocallyRingedSpace 𝒜).restrict ⋯ ⟶
                  AlgebraicGeometry.Spec.locallyRingedSpaceObj (CommRingCat.of (HomogeneousLocalization.Away 𝒜 f))

The morphism of locally ringed space from Proj|D(f) to Spec A⁰_f induced by the ring map A⁰_ f → Γ(Proj, D(f)) under the gamma spec adjunction.

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme

Cited by

13 results in Mathlib

Foundations

Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing