The Stacks project

Definition 17.10.6. In the situation of Lemma 17.10.5 we say $\mathcal{F}_ M$ is the sheaf associated to the module $M$ and the ring map $\alpha$. If $R = \Gamma (X, \mathcal{O}_ X)$ and $\alpha = \text{id}_ R$ we simply say $\mathcal{F}_ M$ is the sheaf associated to the module $M$.