Lemma 29.20.5. Let $f : X \to S$ be a morphism of schemes. Let $x \in X$ be a point. Set $s = f(x)$. If $f$ is quasi-finite at $x$, then the residue field extension $\kappa (s) \subset \kappa (x)$ is finite.
Proof. This is clear from Algebra, Definition 10.122.3. $\square$
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