Theorems · Definition · algebraic geometry

AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.structureSheafInType

{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.Sheaf (Type u_1) (ProjectiveSpectrum.top 𝒜)

The structure sheaf (valued in Type, not yet CommRing) is the subsheaf consisting of functions satisfying isLocallyFraction.

Defined in: Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf
Cited by: 2 results in Mathlib
Foundations: Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing SetLike AddSubgroupClass GradedRing

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Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CommRingstatement and proof · cited by 17,173
SetLikestatement and proof · cited by 1,084
GradedRingstatement and proof · cited by 424
AddSubgroupClassstatement and proof · cited by 240
TopCat.Sheafstatement · cited by 73
ProjectiveSpectrum.topstatement · cited by 32
AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.isLocallyFractionproof · cited by 20
TopCat.subsheafToTypesproof · cited by 5

Cited by5

Results whose statement or proof uses this declaration.

AlgebraicGeometry.openToLocalizationproof · cited by 1
AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.structurePresheafInCommRingproof · cited by 1
AlgebraicGeometry.Proj.sheafedSpaceMap_hom_c_app_hom_apply_coestatement · cited by 0
AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.structurePresheafCompForgetstatement · cited by 0
AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.structurePresheafInCommRing_obj_carrierstatement · cited by 0