Definition 63.14.1. Let $\Lambda $ be a finite ring, $X$ a projective curve over a finite field $k$ and $K \in D_{ctf}(X, \Lambda )$ (for instance $K = \underline\Lambda $). There is a canonical map $c_ K : \pi _ X^{-1}K \to K$, and its base change $c_ K|_{X_{\bar k}}$ induces an action denoted $\pi _ X^*$ on the perfect complex $R\Gamma (X_{\bar k}, K|_{X_{\bar k}})$. The *global Lefschetz number* of $K$ is the trace $\text{Tr}(\pi _ X^* |_{R\Gamma (X_{\bar k}, K)})$ of that action. It is an element of $\Lambda ^\natural $.

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