Definition 111.36.1. Let $X$ be a scheme. A sheaf $\mathcal{F}$ of $\mathcal{O}_ X$-modules is *quasi-coherent* if for every affine open $\mathop{\mathrm{Spec}}(R) = U \subset X$ the restriction $\mathcal{F}|_ U$ is of the form $\widetilde M$ for some $R$-module $M$.

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