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Theorems · Definition · algebraic geometry

AlgebraicGeometry.StructureSheaf.Localizations

{R : Type u} →
  (M : Type u) →
    [inst : CommRing R] → [inst_1 : AddCommGroup M] → [Module R M] → ↑(AlgebraicGeometry.PrimeSpectrum.Top R) → Type u

The type family over PrimeSpectrum R consisting of the localization over each point.

Defined in
Mathlib.AlgebraicGeometry.StructureSheaf
Cited by
15 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingAddCommGroupModule

Around this declaration

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

AlgebraicGeometry.StructureSheaf.isLocallyFraction · cited by 8StructureSheaf.isLocallyF…AlgebraicGeometry.StructureSheaf.comap_apply · cited by 5StructureSheaf.comap_applyAlgebraicGeometry.StructureSheaf.toOpen_comp_comap · cited by 3StructureSheaf.toOpen_com…AlgebraicGeometry.StructureSheaf.Localizations.comapFun · cited by 3Localizations.comapFunAlgebraicGeometry.StructureSheaf.Localizations.comapFun_mk · cited by 3Localizations.comapFun_mkAlgebraicGeometry.StructureSheaf.comapFun · cited by 2StructureSheaf.comapFunAlgebraicGeometry.StructureSheaf.isFractionPrelocal · cited by 2StructureSheaf.isFraction…AlgebraicGeometry.StructureSheaf.comap_comp · cited by 1StructureSheaf.comap_compAlgebraicGeometry.Spec_Γ_naturality · cited by 1AlgebraicGeometry.Spec_Γ_…AlgebraicGeometry.StructureSheaf.comap_id_eq_map · cited by 1StructureSheaf.comap_id_e…AlgebraicGeometry.StructureSheaf.comapₗ_eq_localRingHom · cited by 1StructureSheaf.comapₗ_eq_…AlgebraicGeometry.StructureSheaf.const_apply · cited by 1StructureSheaf.const_applyAlgebraicGeometry.structureSheafInType.add_apply · cited by 0structureSheafInType.add_…AlgebraicGeometry.structureSheafInType.mul_apply · cited by 0structureSheafInType.mul_…AlgebraicGeometry.structureSheafInType.smul_apply · cited by 0structureSheafInType.smul…Module · cited by 20661ModuleCommRing · cited by 17173CommRingAddCommGroup · cited by 12871AddCommGroupTopCat.carrier · cited by 3184TopCat.carrierIdeal.primeCompl · cited by 462Ideal.primeComplPrimeSpectrum.asIdeal · cited by 333PrimeSpectrum.asIdealLocalizedModule · cited by 154LocalizedModuleAlgebraicGeometry.PrimeSpectrum.Top · cited by 104PrimeSpectrum.TopStructureSheaf.LocalizationsCITED BYCITES

Cites8

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Cited by23

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