Definition 17.9.1. 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 of finite type if for every $x \in X$ there exists an open neighbourhood $U$ such that $\mathcal{F}|_ U$ is generated by finitely many sections.

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