Theorems · Theorem · commutative algebra
Algebra.FormallyEtale.localization_map
∀ {R : Type u_2} {S : Type u_3} {Rₘ : Type u_4} {Sₘ : Type u_5} [inst : CommRing R] [inst_1 : CommRing S]
[inst_2 : CommRing Rₘ] [inst_3 : CommRing Sₘ] (M : Submonoid R) [inst_4 : Algebra R S] [inst_5 : Algebra R Sₘ]
[inst_6 : Algebra S Sₘ] [inst_7 : Algebra R Rₘ] [inst_8 : Algebra Rₘ Sₘ] [IsScalarTower R Rₘ Sₘ]
[IsScalarTower R S Sₘ] [IsLocalization M Rₘ] [IsLocalization (Submonoid.map (algebraMap R S) M) Sₘ]
[Algebra.FormallyEtale R S], Algebra.FormallyEtale Rₘ SₘThe localization of a formally étale map is formally étale.
- Defined in
- Mathlib.RingTheory.Etale.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 132 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
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- Submonoid.mapstatement and proof · cited by 190
- Algebra.FormallyEtalestatement and proof · cited by 37
- Algebra.FormallyEtale.compproof · cited by 5
- Algebra.FormallyEtale.of_isLocalizationproof · cited by 3
- Algebra.FormallyEtale.localization_baseproof · cited by 2
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