Lemma 37.58.5. Let f : X \to S be a morphism of schemes which is locally of finite type. Let \mathcal{F} be a quasi-coherent \mathcal{O}_ X-module. Let S' \to S be a morphism of schemes, set X' = X \times _ S S' and denote \mathcal{F}' the pullback of \mathcal{F} to X'. If \mathcal{F} is of finite presentation relative to S, then \mathcal{F}' is of finite presentation relative to S'.
Proof. Translation of the result of More on Algebra, Lemma 15.80.5 into the language of schemes. \square
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