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Theorems · Definition · algebraic geometry

ProjectiveSpectrum.asHomogeneousIdeal

{A : Type u_1} →
  {σ : Type u_2} →
    [inst : CommRing A] →
      [inst_1 : SetLike σ A] →
        [inst_2 : AddSubmonoidClass σ A] →
          {𝒜 : ℕ → σ} → [inst_3 : GradedRing 𝒜] → ProjectiveSpectrum 𝒜 → HomogeneousIdeal 𝒜
Defined in
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology
Cited by
61 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext
Assumes
CommRingSetLikeAddSubmonoidClassGradedRing

Around this declaration

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

ProjectiveSpectrum.basicOpen · cited by 48ProjectiveSpectrum.basicO…ProjectiveSpectrum.zeroLocus · cited by 42ProjectiveSpectrum.zeroLo…AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.isLocallyFraction · cited by 20StructureSheaf.isLocallyF…ProjectiveSpectrum.vanishingIdeal · cited by 20ProjectiveSpectrum.vanish…AlgebraicGeometry.Proj.stalkIso' · cited by 7Proj.stalkIso'AlgebraicGeometry.sectionInBasicOpen · cited by 6AlgebraicGeometry.section…AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.mk_mem_carrier · cited by 5ToSpec.mk_mem_carrierAlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.carrier · cited by 5ToSpec.carrierAlgebraicGeometry.mem_basicOpen_den · cited by 5AlgebraicGeometry.mem_bas…AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.isFractionPrelocal · cited by 5StructureSheaf.isFraction…AlgebraicGeometry.stalkToFiberRingHom · cited by 4AlgebraicGeometry.stalkTo…ProjectiveSpectrum.mem_zeroLocus · cited by 4ProjectiveSpectrum.mem_ze…AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq · cited by 3Proj.toSpec_base_apply_eqAlgebraicGeometry.stalkToFiberRingHom_germ · cited by 3AlgebraicGeometry.stalkTo…AlgebraicGeometry.Proj.comapStructureSheafFun · cited by 3Proj.comapStructureSheafF…CommRing · cited by 17173CommRingSetLike · cited by 1084SetLikeGradedRing · cited by 424GradedRingAddSubmonoidClass · cited by 346AddSubmonoidClassHomogeneousIdeal · cited by 115HomogeneousIdealProjectiveSpectrum · cited by 86ProjectiveSpectrumProjectiveSpectrum.asHomogene…CITED BYCITES

Cites6

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Cited by78

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