The Stacks project

Definition 66.29.1. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. A quasi-coherent $\mathcal{O}_ X$-module is a quasi-coherent module on the ringed site $(X_{\acute{e}tale}, \mathcal{O}_ X)$ in the sense of Modules on Sites, Definition 18.23.1. The category of quasi-coherent sheaves on $X$ is denoted $\mathit{QCoh}(\mathcal{O}_ X)$.

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View Definition 66.29.1 as pdf