The Stacks project

Definition 18.32.6. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. The Picard group $\mathop{\mathrm{Pic}}\nolimits (\mathcal{O})$ of the ringed site is the abelian group whose elements are isomorphism classes of invertible $\mathcal{O}$-modules, with addition corresponding to tensor product.

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