Lemma 61.51.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. If $f$ is locally quasi-finite and separated, then $f$ is representable.

**Proof.**
This is immediate from Proposition 61.50.2 and the fact that being locally quasi-finite and separated is preserved under any base change, see Lemmas 61.27.4 and 61.4.4.
$\square$

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