Definition
(See Stacks 01B4). 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 neighborhood \(U\) such that \(\mathcal F|_U\) is generated by finitely many sections.