Lemma 74.6.2. Let X be an algebraic space over a scheme S. Let \mathcal{F} be a quasi-coherent \mathcal{O}_ X-module. Let \{ f_ i : X_ i \to X\} _{i \in I} be an fpqc covering such that each f_ i^*\mathcal{F} is an \mathcal{O}_{X_ i}-module of finite presentation. Then \mathcal{F} is an \mathcal{O}_ X-module of finite presentation.
Proof. This follows from the case of schemes, see Descent, Lemma 35.7.3, by étale localization. \square
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