Theorems · Definition · commutative algebra
HomogeneousLocalization.Away
{ι : Type u_1} → {A : Type u_2} → {σ : Type u_3} → [CommRing A] → [SetLike σ A] → (ι → σ) → A → Type (max u_1 u_2)Localizing away from powers of f homogeneously.
- Cited by
- 105 results in Mathlib
- Foundations
- Depth 25 from the axioms, rests on 379 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- SetLikestatement and proof · cited by 1,084
- Submonoid.powersproof · cited by 408
- HomogeneousLocalizationproof · cited by 69
Cited by132
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Proj.awayιstatement · cited by 30
- HomogeneousLocalization.awayMapstatement and proof · cited by 27
- AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpecstatement and proof · cited by 13
- AlgebraicGeometry.Proj.pullbackAwayιIsostatement · cited by 12
- AlgebraicGeometry.Proj.basicOpenIsoSpecstatement · cited by 11
- HomogeneousLocalization.Away.mkstatement · cited by 11
- HomogeneousLocalization.Away.mapstatement · cited by 10
- AlgebraicGeometry.Proj.awayToSectionstatement · cited by 9
- AlgebraicGeometry.ProjIsoSpecTopComponent.toSpecstatement · cited by 9
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrierstatement and proof · cited by 9
- AlgebraicGeometry.Proj.toBasicOpenOfGlobalSectionsproof · cited by 7
- AlgebraicGeometry.Proj.SpecMap_awayMap_awayιstatement and proof · cited by 5