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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