The Stacks project

Definition 17.11.1. 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 presentation if for every point $x \in X$ there exists an open neighbourhood $x\in U \subset X$, and $n, m \in \mathbf{N}$ such that $\mathcal{F}|_ U$ is isomorphic to the cokernel of a map