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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