Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsPreimmersion.of_isLocalization
∀ {R S : Type u} [inst : CommRing R] (M : Submonoid R) [inst_1 : CommRing S] [inst_2 : Algebra R S]
[IsLocalization M S],
AlgebraicGeometry.IsPreimmersion (AlgebraicGeometry.Spec.map (CommRingCat.ofHom (algebraMap R S)))- Cited by
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- Foundations
- Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- Algebrastatement and proof · cited by 11,388
- Algebra.algebraMapstatement · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- AlgebraicGeometry.Specstatement · cited by 626
- AlgebraicGeometry.Spec.mapstatement · cited by 332
- CommRingCat.ofHomstatement · cited by 259
- AlgebraicGeometry.IsPreimmersionstatement · cited by 14
- RingHom.surjectiveOnStalks_of_isLocalizationproof · cited by 3
- PrimeSpectrum.localization_comap_isEmbeddingproof · cited by 2
- AlgebraicGeometry.IsPreimmersion.mk_SpecMapproof · cited by 1
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