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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.homogeneousLocalizationToStalk_stalkToFiberRingHom

∀ {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))
  (z : ↑((AlgebraicGeometry.ProjectiveSpectrum.Proj.structureSheaf 𝒜).presheaf.stalk x)),
  AlgebraicGeometry.homogeneousLocalizationToStalk 𝒜 x
      ((CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.stalkToFiberRingHom 𝒜 x)) z) =
    z
Defined in
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf
Cited by
0 results in Mathlib
Foundations
Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingSetLikeAddSubgroupClassGradedRing
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AlgebraicGeometry.Proj.stalkIso' · cited by 7Proj.stalkIso'DFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCommRing · cited by 17173CommRingRingHom · cited by 10189RingHomCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierCommRingCat · cited by 2333CommRingCatOpposite.unop · cited by 2231Opposite.unopTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensQuiver.Hom.op · cited by 1948Hom.opCommRingCat.carrier · cited by 1096CommRingCat.carrierSetLike · cited by 1084SetLikeQuiver.Hom.unop · cited by 903Hom.unopAlgebraicGeometry.homogeneous…CITED BYCITES

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