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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Proj.toLocallyRingedSpace

{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.LocallyRingedSpace

Proj of a graded ring as a LocallyRingedSpace

Defined in
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf
Cited by
26 results in Mathlib
Foundations
Depth 130 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 · cited by 63AlgebraicGeometry.ProjAlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec · cited by 13Proj.toSpecAlgebraicGeometry.ProjIsoSpecTopComponent.toSpec · cited by 9ProjIsoSpecTopComponent.t…AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.carrier · cited by 5ToSpec.carrierAlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.mk_mem_carrier · cited by 5ToSpec.mk_mem_carrierAlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ · cited by 5Proj.awayToΓAlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.toFun · cited by 4FromSpec.toFunAlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.toFun · cited by 3ToSpec.toFunAlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq · cited by 3Proj.toSpec_base_apply_eqAlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.preimage_basicOpen · cited by 2ToSpec.preimage_basicOpenAlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalk · cited by 2Proj.awayToΓ_ΓToStalkAlgebraicGeometry.ProjectiveSpectrum.Proj.specStalkEquiv · cited by 2Proj.specStalkEquivAlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec · cited by 2Proj.toStalk_stalkMap_toS…AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_injective · cited by 2ProjIsoSpecTopComponent.t…AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_surjective · cited by 2ProjIsoSpecTopComponent.t…CommRing · cited by 17173CommRingCommRingCat · cited by 2333CommRingCatSetLike · cited by 1084SetLikeGradedRing · cited by 424GradedRingAddSubgroupClass · cited by 240AddSubgroupClassAlgebraicGeometry.LocallyRingedSpace · cited by 205AlgebraicGeometry.Locally…AlgebraicGeometry.SheafedSpace · cited by 142AlgebraicGeometry.Sheafed…AlgebraicGeometry.Proj.toSheafedSpace · cited by 5Proj.toSheafedSpaceProj.toLocallyRingedSpaceCITED BYCITES

Cites8

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Cited by37

Results whose statement or proof uses this declaration.