The Stacks project

Definition 17.25.9. Let $(X, \mathcal{O}_ X)$ be a ringed space. The Picard group $\mathop{\mathrm{Pic}}\nolimits (X)$ of $X$ is the abelian group whose elements are isomorphism classes of invertible $\mathcal{O}_ X$-modules, with addition corresponding to tensor product.