Theorems · Definition · algebraic geometry

AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection

{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) →
                CommRingCat.of (HomogeneousLocalization.Away 𝒜 f) ⟶
                  (AlgebraicGeometry.ProjectiveSpectrum.Proj.structureSheaf 𝒜).obj.obj
                    (Opposite.op (ProjectiveSpectrum.basicOpen 𝒜 f))

The ring map from A⁰_ f to the local sections of the structure sheaf of the projective spectrum of A on the basic open set D(f) defined by sending s ∈ A⁰_f to the section x ↦ s on D(f).

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme

Cited by

3 results in Mathlib

Foundations

Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing