Theorems · Theorem · commutative algebra
Algebra.FormallyEtale.of_isLocalization
∀ {R : Type u_2} {Rₘ : Type u_4} [inst : CommRing R] [inst_1 : CommRing Rₘ] (M : Submonoid R) [inst_2 : Algebra R Rₘ]
[IsLocalization M Rₘ], Algebra.FormallyEtale R Rₘ- Defined in
- Mathlib.RingTheory.Etale.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- Algebra.FormallyEtalestatement · cited by 37
- Algebra.FormallyEtale.iff_formallyUnramified_and_formallySmoothproof · cited by 8
- Algebra.FormallySmooth.of_isLocalizationproof · cited by 6
- Algebra.FormallyUnramified.of_isLocalizationproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.FormallySmooth.of_formallySmooth_residueField_tensorproof · cited by 1
- Algebra.FormallyEtale.localization_mapproof · cited by 0
- Algebra.Etale.of_isLocalizationAwayproof · cited by 0