Lemma 76.7.14 (05ZE)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 76: More on Morphisms of Spaces
Section 76.7: Sheaf of differentials of a morphism
Lemma 76.7.14 (cite)

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Lemma 76.7.14. 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 76.7.3. $\square$

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