Definition 17.25.1. Let $(X, \mathcal{O}_ X)$ be a ringed space. An *invertible $\mathcal{O}_ X$-module* is a sheaf of $\mathcal{O}_ X$-modules $\mathcal{L}$ such that the functor

is an equivalence of categories. We say that $\mathcal{L}$ is *trivial* if it is isomorphic as an $\mathcal{O}_ X$-module to $\mathcal{O}_ X$.

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