Theorems · Definition · algebraic geometry

AlgebraicGeometry.homogeneousLocalizationToStalk

{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)) →
                HomogeneousLocalization.AtPrime 𝒜 x.asHomogeneousIdeal.toIdeal →
                  ↑((AlgebraicGeometry.ProjectiveSpectrum.Proj.structureSheaf 𝒜).presheaf.stalk x)

Given any point x and f in the homogeneous localization at x, there is an element in the stalk at x obtained by sectionInBasicOpen. This is the inverse of stalkToFiberRingHom.

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf

Cited by

2 results in Mathlib

Foundations

Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing