Lemma 29.32.13 (01V3)—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 29.32.13 (cite)

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Lemma 29.32.13. Let $f : X \to S$ be a morphism of schemes. If $f$ is locally of finite presentation, then $\Omega _{X/S}$ is an $\mathcal{O}_ X$ -module of finite presentation.

Proof. Immediate from Algebra, Lemma 10.131.15, Lemma 29.32.5, Lemma 29.21.2, and Properties, Lemma 28.16.2. $\square$

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Comment #1815 by Keenan Kidwell on February 03, 2016 at 01:16

The map $f$ should be assumed locally of finite presentation here I think.

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