Theorems · Theorem · algebraic geometry
PrimeSpectrum.localization_comap_range
∀ {R : Type u} (S : Type v) [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S] (M : Submonoid R)
[IsLocalization M S], Set.range (PrimeSpectrum.comap (algebraMap R S)) = {p | Disjoint ↑M ↑p.asIdeal}- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Set.ofPredstatement and proof · cited by 6,101
- Idealstatement · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Set.rangestatement and proof · cited by 4,705
- Submonoidstatement and proof · cited by 3,086
- Set.extproof · cited by 2,266
- Disjointstatement and proof · cited by 2,201
- Ideal.mapproof · cited by 692
Cited by2
Results whose statement or proof uses this declaration.
- PrimeSpectrum.localization_away_comap_rangeproof · cited by 17
- Module.rankAtStalk_eq_of_le_of_finite_of_flatproof · cited by 1