Theorems · Theorem · commutative algebra

Algebra.FormallySmooth.kerCotangentToTensor_injective_iff

∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {P : Type u_2}
  [inst_3 : CommRing P] [inst_4 : Algebra R P] [Algebra.FormallySmooth R P] [inst_6 : Algebra P A]
  [IsScalarTower R P A],
  Function.Surjective ⇑(algebraMap P A) →
    (Function.Injective ⇑(KaehlerDifferential.kerCotangentToTensor R P A) ↔ Subsingleton (Algebra.H1Cotangent R A))

Defined in

Mathlib.RingTheory.Smooth.Basic

Cited by

1 results in Mathlib

Foundations

Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebra.FormallySmoothAlgebraIsScalarTower