Lemma 37.58.4. Let \pi : X \to Y be a finite morphism of schemes locally of finite type over a base scheme S. Let \mathcal{F} be a quasi-coherent \mathcal{O}_ X-module. Then \mathcal{F} is of finite presentation relative to S if and only if \pi _*\mathcal{F} is of finite presentation relative to S.
Proof. Translation of the result of More on Algebra, Lemma 15.80.3 into the language of schemes. \square
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