Definition 17.8.1. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $\mathcal{F}$ be a sheaf of $\mathcal{O}_ X$-modules. We say that $\mathcal{F}$ is *locally generated by sections* if for every $x \in X$ there exists an open neighbourhood $U$ of $x$ such that $\mathcal{F}|_ U$ is globally generated as a sheaf of $\mathcal{O}_ U$-modules.

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