Theorems · Definition · algebraic geometry

AlgebraicGeometry.sectionInBasicOpen

{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] →
              (x : ↑(ProjectiveSpectrum.top 𝒜)) →
                (f : HomogeneousLocalization.NumDenSameDeg 𝒜 x.asHomogeneousIdeal.toIdeal.primeCompl) →
                  ↑((AlgebraicGeometry.ProjectiveSpectrum.Proj.structureSheaf 𝒜).obj.obj
                      (Opposite.op (ProjectiveSpectrum.basicOpen 𝒜 ↑f.den)))

Given a point x corresponding to a homogeneous prime ideal, there is a (dependent) function such that, for any f in the homogeneous localization at x, it returns the obvious section in the basic open set D(f.den).

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf

Cited by

6 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing