Theorems · Definition · algebraic geometry

AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.isLocallyFraction

{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.LocalPredicate fun x => HomogeneousLocalization.AtPrime 𝒜 x.asHomogeneousIdeal.toIdeal

We will define the structure sheaf as the subsheaf of all dependent functions in Π x : U, HomogeneousLocalization 𝒜 x consisting of those functions which can locally be expressed as a ratio of A of same grading.

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf

Cited by

20 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing