Theorems · Theorem · commutative algebra
Algebra.formallyEtale_iff
∀ (R : Type u) (A : Type v) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A], Algebra.FormallyEtale R A ↔ Subsingleton Ω[A⁄R] ∧ Subsingleton (Algebra.H1Cotangent 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
- KaehlerDifferentialstatement and proof · cited by 204
- Algebra.FormallyEtalestatement and proof · cited by 37
- Algebra.H1Cotangentstatement and proof · cited by 27
- Algebra.FormallyEtale.casesOnproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.basicOpen_subset_etaleLocus_iffproof · cited by 3
- Algebra.etaleLocus_eq_compl_supportproof · cited by 2
- Algebra.etaleLocus_eq_univ_iffproof · cited by 1