The Stacks project

Lemma 75.7.14. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. If $f$ is locally of finite type, then $\Omega _{X/Y}$ is a finite type $\mathcal{O}_ X$-module.

Proof. Follows from the schemes version, see Morphisms, Lemma 29.32.12 and étale localization, see Lemma 75.7.3. $\square$

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