Theorems · Theorem · algebraic geometry
RingHom.etale_iff_formallyUnramified_and_smooth
∀ {R : Type u_3} {S : Type u_4} [inst : CommRing R] [inst_1 : CommRing S] (f : R →+* S),
f.Etale ↔ f.FormallyUnramified ∧ f.Smooth- Defined in
- Mathlib.RingTheory.RingHom.Etale
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Algebraproof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- RingHom.toAlgebraproof · cited by 337
- Algebra.FormallyUnramifiedproof · cited by 75
- Algebra.Etaleproof · cited by 34
- RingHom.Smoothstatement · cited by 30
- RingHom.Etalestatement · cited by 26
- RingHom.FormallyUnramifiedstatement · cited by 26
- Algebra.Smoothproof · cited by 22
- Algebra.FormallyEtale.of_formallyUnramified_and_formallySmoothproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- RingHom.Etale.eq_formallyUnramified_and_smoothproof · cited by 3
- RingHom.Etale.of_bijectiveproof · cited by 1
- RingHom.Etale.formallyUnramifiedproof · cited by 0