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Theorems · Theorem · commutative algebra

Algebra.Etale.of_etale_tensorProduct_of_faithfullyFlat

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (T : Type u_3)
  [inst_3 : CommRing T] [inst_4 : Algebra R T] [Module.FaithfullyFlat R T] [Algebra.Etale T (TensorProduct R T S)],
  Algebra.Etale R S
Defined in
Mathlib.RingTheory.Etale.Descent
Cited by
1 results in Mathlib
Foundations
Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraCommRingAlgebraModule.FaithfullyFlatAlgebra.Etale
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Around this declaration

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RingHom.Etale.codescendsAlong_faithfullyFlat · cited by 0Etale.codescendsAlong_fai…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraTensorProduct · cited by 2545TensorProductModule.FaithfullyFlat · cited by 72Module.FaithfullyFlatAlgebra.Etale · cited by 34Algebra.EtaleAlgebra.FormallyUnramified.of_formallyUnramified_tensorProduct_of_faithfullyFlat · cited by 3FormallyUnramified.of_for…Algebra.Smooth.of_smooth_tensorProduct_of_faithfullyFlat · cited by 2Smooth.of_smooth_tensorPr…Algebra.Etale.iff_formallyUnramified_and_smooth · cited by 1Etale.iff_formallyUnramif…Etale.of_etale_tensorProduct_…CITED BYCITES

Cites8

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Cited by1

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