Lemma 10.158.6. Let $K/k$ be an extension of fields. Then $K$ is formally smooth over $k$ if and only if $H_1(L_{K/k}) = 0$.
Proof. This follows from Proposition 10.138.8 and the fact that a vector spaces is free (hence projective). $\square$
Lemma 10.158.6. Let $K/k$ be an extension of fields. Then $K$ is formally smooth over $k$ if and only if $H_1(L_{K/k}) = 0$.
Proof. This follows from Proposition 10.138.8 and the fact that a vector spaces is free (hence projective). $\square$
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