Theorems · Theorem · algebraic geometry
PrimeSpectrum.localization_away_isOpenEmbedding
∀ {R : Type u} [inst : CommSemiring R] (S : Type v) [inst_1 : CommSemiring S] [inst_2 : Algebra R S] (r : R)
[IsLocalization.Away r S], Topology.IsOpenEmbedding (PrimeSpectrum.comap (algebraMap R S))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsOpenproof · cited by 2,400
- PrimeSpectrumstatement and proof · cited by 625
- Submonoid.powersproof · cited by 408
- Topology.IsEmbeddingproof · cited by 294
- Topology.IsOpenEmbeddingstatement · cited by 231
- IsLocalization.Awaystatement and proof · cited by 218
- PrimeSpectrum.comapstatement and proof · cited by 199
- PrimeSpectrum.localization_away_comap_rangeproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.isOpen_smoothLocusproof · cited by 2