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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Proj

{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.Scheme

This is the scheme Proj(A) for any -graded ring A.

Defined in
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme
Cited by
63 results in Mathlib
Foundations
Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingSetLikeAddSubgroupClassGradedRing

Around this declaration

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

AlgebraicGeometry.Proj.basicOpen · cited by 38Proj.basicOpenAlgebraicGeometry.Proj.awayι · cited by 30Proj.awayιAlgebraicGeometry.Proj.pullbackAwayιIso · cited by 12Proj.pullbackAwayιIsoAlgebraicGeometry.Proj.basicOpenIsoSpec · cited by 11Proj.basicOpenIsoSpecAlgebraicGeometry.Proj.awayToSection · cited by 9Proj.awayToSectionAlgebraicGeometry.Proj.map · cited by 9Proj.mapAlgebraicGeometry.Proj.toBasicOpenOfGlobalSections · cited by 7Proj.toBasicOpenOfGlobalS…AlgebraicGeometry.Proj.fromOfGlobalSections · cited by 6Proj.fromOfGlobalSectionsAlgebraicGeometry.Proj.SpecMap_awayMap_awayι · cited by 5Proj.SpecMap_awayMap_awayιAlgebraicGeometry.Proj.basicOpenToSpec · cited by 5Proj.basicOpenToSpecAlgebraicGeometry.Proj.basicOpen_mono · cited by 5Proj.basicOpen_monoAlgebraicGeometry.Proj.toSpecZero · cited by 5Proj.toSpecZeroAlgebraicGeometry.Proj.affineOpenCover · cited by 4Proj.affineOpenCoverAlgebraicGeometry.Proj.awayι_comp_map · cited by 3Proj.awayι_comp_mapAlgebraicGeometry.Proj.awayι_toSpecZero · cited by 3Proj.awayι_toSpecZeroCommRing · cited by 17173CommRingTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…SetLike · cited by 1084SetLikeGradedRing · cited by 424GradedRingAddSubgroupClass · cited by 240AddSubgroupClassAlgebraicGeometry.LocallyRingedSpace · cited by 205AlgebraicGeometry.Locally…AlgebraicGeometry.Proj.toLocallyRingedSpace · cited by 26Proj.toLocallyRingedSpaceAlgebraicGeometry.ProjCITED BYCITES

Cites11

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

Cited by78

Results whose statement or proof uses this declaration.