64.3.10.1
\begin{equation} \label{trace-equation-trace-formula-second} \sum \nolimits _{x \in X(k)} \text{Tr}(\pi _ x | \mathcal{F}_{\bar x}) = \sum \nolimits _{i = 0}^2 (-1)^ i \text{Tr}(\pi _ X^* | H^ i_ c(X_{\bar k}, \mathcal{F})) \end{equation}
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