Theorems · Theorem · commutative algebra
Algebra.FormallyEtale.of_formallyUnramified_and_formallySmooth
∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
[Algebra.FormallyUnramified R A] [Algebra.FormallySmooth R A], Algebra.FormallyEtale R A- Defined in
- Mathlib.RingTheory.Etale.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.FormallyUnramifiedstatement and proof · cited by 75
- Algebra.FormallySmoothstatement and proof · cited by 60
- Algebra.FormallyEtalestatement · cited by 37
- Algebra.FormallyEtale.iff_formallyUnramified_and_formallySmoothproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.FormallyEtale.of_restrictScalarsproof · cited by 4
- RingHom.etale_iff_formallyUnramified_and_smoothproof · cited by 3
- Algebra.FormallyEtale.iff_comp_bijectiveproof · cited by 2