Let $X/k$ be a variety over a field $k$ and let $\varphi:X\rightarrow X$ be a proper endomorphism. If $F$ is an $\ell $-adic
sheaf on $X$ with a map $u:\varphi ^*F\rightarrow F$ then one obtains an endomorphism of the compactly supported cohomology $H_c(X, F)$. When $X$ is proper the Lefschetz-Verdier trace formula relates the trace of this endomorphism to certain local terms
$Tr(c,Z)$ associated to the connected components $Z$ (over $\bar k$) of the fixed point scheme of $\varphi $.