The Stacks project

Definition 111.36.6. Let $X$ be a locally Noetherian scheme. Let $\mathcal{F}$ be a quasi-coherent sheaf of $\mathcal{O}_ X$-modules. We say $\mathcal{F}$ is coherent if for every point $x \in X$ there exists an affine open $\mathop{\mathrm{Spec}}(R) = U \subset X$ such that $\mathcal{F}|_ U$ is isomorphic to $\widetilde M$ for some finite $R$-module $M$.