Formally smooth equals separable for field extensions.

Lemma 10.158.8. Let $k$ be a field.

1. If the characteristic of $k$ is zero, then any extension field of $k$ is formally smooth over $k$.

2. If the characteristic of $k$ is $p > 0$, then $K/k$ is formally smooth if and only if it is a separable field extension.

Comment #1034 by Matthew Emerton on

Suggested slogan: Formally smooth equals separable for field extensions

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