Theorems · Definition · algebraic geometry

AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.sectionsSubring

{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))ᵒᵖ) →
                Subring ((x : ↥(Opposite.unop U)) → HomogeneousLocalization.AtPrime 𝒜 (↑x).asHomogeneousIdeal.toIdeal)

The functions satisfying isLocallyFraction form a subring of all dependent functions Π x : U, HomogeneousLocalization 𝒜 x.

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf

Cited by

0 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing