Lemma 66.51.1. 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 66.50.2 and the fact that being locally quasi-finite and separated is preserved under any base change, see Lemmas 66.27.4 and 66.4.4. $\square$
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