Lemma 37.58.6. Let $X \to Y \to S$ be morphisms of schemes which are locally of finite type. Let $\mathcal{G}$ be a quasi-coherent $\mathcal{O}_ Y$-module. If $f : X \to Y$ is locally of finite presentation and $\mathcal{G}$ of finite presentation relative to $S$, then $f^*\mathcal{G}$ is of finite presentation relative to $S$.
Proof. Translation of the result of More on Algebra, Lemma 15.80.6 into the language of schemes. $\square$
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