Lemma 29.32.12 (01V2)—The Stacks project

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Part 2: Schemes
Chapter 29: Morphisms of Schemes
Section 29.32: Sheaf of differentials of a morphism
Lemma 29.32.12 (cite)

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Lemma 29.32.12. Let $f : X \to S$ be a morphism of schemes. If $f$ is locally of finite type, then $\Omega _{X/S}$ is a finite type $\mathcal{O}_ X$ -module.

Proof. Immediate from Algebra, Lemma 10.131.16, Lemma 29.32.5, Lemma 29.15.2, and Properties, Lemma 28.16.1. $\square$

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