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 uThe 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- TopCat.carrierstatement and proof · cited by 3,184
- Ideal.primeComplproof · cited by 462
- PrimeSpectrum.asIdealproof · cited by 333
- LocalizedModuleproof · cited by 154
- AlgebraicGeometry.PrimeSpectrum.Topstatement and proof · cited by 104
Cited by23
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.StructureSheaf.isLocallyFractionstatement · cited by 8
- AlgebraicGeometry.StructureSheaf.comap_applystatement · cited by 5
- AlgebraicGeometry.StructureSheaf.toOpen_comp_comapproof · cited by 3
- AlgebraicGeometry.StructureSheaf.Localizations.comapFunstatement · cited by 3
- AlgebraicGeometry.StructureSheaf.Localizations.comapFun_mkstatement and proof · cited by 3
- AlgebraicGeometry.StructureSheaf.comapFunstatement and proof · cited by 2
- AlgebraicGeometry.StructureSheaf.isFractionPrelocalstatement and proof · cited by 2
- AlgebraicGeometry.StructureSheaf.comap_compproof · cited by 1
- AlgebraicGeometry.Spec_Γ_naturalityproof · cited by 1
- AlgebraicGeometry.StructureSheaf.comap_id_eq_mapproof · cited by 1
- AlgebraicGeometry.StructureSheaf.comapₗ_eq_localRingHomstatement and proof · cited by 1
- AlgebraicGeometry.StructureSheaf.const_applystatement · cited by 1