Definition 33.44.1. Let $k$ be a field, let $X$ be a proper scheme of dimension $\leq 1$ over $k$, and let $\mathcal{L}$ be an invertible $\mathcal{O}_ X$-module. The *degree* of $\mathcal{L}$ is defined by

More generally, if $\mathcal{E}$ is a locally free sheaf of rank $n$ we define the *degree* of $\mathcal{E}$ by

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