Theorems · Definition · algebraic geometry

AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.isFractionPrelocal

{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] →
              TopCat.PrelocalPredicate fun x => HomogeneousLocalization.AtPrime 𝒜 x.asHomogeneousIdeal.toIdeal

The predicate IsFraction is "prelocal", in the sense that if it holds on U it holds on any open subset V of U.

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf

Cited by

5 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing