Theorems · Theorem · commutative algebra
Algebra.formallySmooth_iff
∀ (R : Type u) (A : Type v) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A], Algebra.FormallySmooth R A ↔ Module.Projective A Ω[A⁄R] ∧ Subsingleton (Algebra.H1Cotangent R A)
- Defined in
- Mathlib.RingTheory.Smooth.Basic
- Cited by
- 4 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.
Cites7
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
- Module.Projectivestatement and proof · cited by 82
- Algebra.FormallySmoothstatement and proof · cited by 60
- Algebra.H1Cotangentstatement and proof · cited by 27
- Algebra.FormallySmooth.casesOnproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Algebra.FormallySmooth.iff_split_injectionproof · cited by 3
- Algebra.basicOpen_subset_smoothLocus_iffproof · cited by 3
- Algebra.Smooth.of_smooth_tensorProduct_of_faithfullyFlatproof · cited by 2
- Algebra.smoothLocus_eq_compl_support_interproof · cited by 2