Lemma 65.38.7. If $f$ is unramified at $x$ then $f$ is quasi-finite at $x$. In particular, an unramified morphism is locally quasi-finite.

Proof. Via a diagram as in Lemma 65.22.1 this translates into Morphisms, Lemma 29.35.10. $\square$

## Comments (2)

Comment #3021 by Brian Lawrence on

Suggested slogan: An unramified morphism is locally quasi-finite.

Comment #3139 by on

Going to ignore this slogan because it is identical to part of the statement of the lemma.

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