Theorems · Definition · algebraic geometry

AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.IsFraction

{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] →
              {U : TopologicalSpace.Opens ↑(ProjectiveSpectrum.top 𝒜)} →
                ((x : ↥U) → HomogeneousLocalization.AtPrime 𝒜 (↑x).asHomogeneousIdeal.toIdeal) → Prop

The predicate saying that a dependent function on an open U is realised as a fixed fraction r / s of same grading in each of the stalks (which are localizations at various prime ideals).

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf

Cited by

0 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing