The Stacks project

Lemma 66.45.8. A finite morphism of algebraic spaces is quasi-finite.

Proof. Let $f : X \to Y$ be a morphism of algebraic spaces. By Definition 66.45.2 and Lemmas 66.8.8 and 66.27.6 both properties may be checked after base change to an affine over $Y$, i.e., we may assume $Y$ affine. If $f$ is finite then $X$ is a scheme. Hence the result follows from the corresponding result for schemes, see Morphisms, Lemma 29.44.10. $\square$

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