The Stacks project

Lemma 37.55.7. Let $X \to Y \to S$ be morphisms of schemes which are locally of finite type. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module. If $Y \to S$ is locally of finite presentation and $\mathcal{F}$ is of finite presentation relative to $Y$, then $\mathcal{F}$ is of finite presentation relative to $S$.

Proof. Translation of the result of More on Algebra, Lemma 15.80.7 into the language of schemes. $\square$


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