Definition 17.25.1 (01CS)—The Stacks project

Processing math: 100%

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

$\textit{Mod}(\mathcal{O}_ X) \longrightarrow \textit{Mod}(\mathcal{O}_ X),\quad \mathcal{F} \longmapsto \mathcal{L} \otimes _{\mathcal{O}_ X} \mathcal{F}$

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

Comments (0)

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$ ). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Comments (0)

Post a comment