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Theorems · Theorem · commutative algebra

Algebra.FormallyEtale.localization_base

∀ {R : Type u_2} {Rₘ : Type u_4} {Sₘ : Type u_5} [inst : CommRing R] [inst_1 : CommRing Rₘ] [inst_2 : CommRing Sₘ]
  (M : Submonoid R) [inst_3 : Algebra R Sₘ] [inst_4 : Algebra R Rₘ] [inst_5 : Algebra Rₘ Sₘ] [IsScalarTower R Rₘ Sₘ]
  [IsLocalization M Rₘ] [Algebra.FormallyEtale R Sₘ], Algebra.FormallyEtale Rₘ Sₘ
Defined in
Mathlib.RingTheory.Etale.Basic
Cited by
2 results in Mathlib
Foundations
Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingCommRingAlgebraAlgebraAlgebraIsScalarTowerIsLocalizationAlgebra.FormallyEtale
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Around this declaration

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Algebra.FormallyEtale.localization_map · cited by 0FormallyEtale.localizatio…Algebra.IsEtaleAt.comp · cited by 0IsEtaleAt.compCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraIsScalarTower · cited by 3896IsScalarTowerSubmonoid · cited by 3086SubmonoidIsLocalization · cited by 636IsLocalizationAlgebra.FormallyEtale · cited by 37Algebra.FormallyEtaleAlgebra.FormallyEtale.iff_formallyUnramified_and_formallySmooth · cited by 8FormallyEtale.iff_formall…Algebra.FormallyUnramified.localization_base · cited by 2FormallyUnramified.locali…Algebra.FormallySmooth.localization_base · cited by 2FormallySmooth.localizati…FormallyEtale.localization_ba…CITED BYCITES

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Cited by2

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