Definition 17.24.9. 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.

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