Theorems · Definition · algebraic geometry

AlgebraicGeometry.Proj.toSheafedSpace

{A : Type u_1} →
  {σ : Type u_2} →
    [inst : CommRing A] →
      [inst_1 : SetLike σ A] →
        [inst_2 : AddSubgroupClass σ A] → (𝒜 : ℕ → σ) → [GradedRing 𝒜] → AlgebraicGeometry.SheafedSpace CommRingCat

Proj of a graded ring as a SheafedSpace

Defined in: Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf
Cited by: 5 results in Mathlib
Foundations: Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing SetLike AddSubgroupClass GradedRing

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites9

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
CommRingCatstatement · cited by 2,333
CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
SetLikestatement and proof · cited by 1,084
GradedRingstatement and proof · cited by 424
AddSubgroupClassstatement and proof · cited by 240
AlgebraicGeometry.SheafedSpacestatement · cited by 142
ProjectiveSpectrumproof · cited by 86
AlgebraicGeometry.ProjectiveSpectrum.Proj.structureSheafproof · cited by 21

Cited by8

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Proj.toLocallyRingedSpaceproof · cited by 26
AlgebraicGeometry.Proj.mapproof · cited by 9
AlgebraicGeometry.Proj.sheafedSpaceMapstatement and proof · cited by 5
AlgebraicGeometry.Proj.germ_map_sectionInBasicOpenstatement · cited by 1
AlgebraicGeometry.Proj.localRingHom_comp_stalkIsostatement and proof · cited by 1
AlgebraicGeometry.Proj.sheafedSpaceMap_hom_base_hom_apply_asHomogeneousIdeal_carrierstatement · cited by 0
AlgebraicGeometry.Proj.sheafedSpaceMap_hom_c_app_hom_apply_coestatement and proof · cited by 0
AlgebraicGeometry.Proj.localRingHom_comp_stalkIso_applystatement · cited by 0