A Lefschetz trace formula is proved for $p^n$-torsion \'etale cohomology of open algebraic varieties defined over a finite field of characteristic $p$. These are analogues of Deligne's conjecture on Lefschetz trace formula for $\ell$-adic cohomology, which was proved by Fujiwara.
"A Lefschetz Trace Formula for $p^n$-torsion \'Etale Cohomology." Tokyo J. Math. 37 (2) 449 - 471, December 2014. https://doi.org/10.3836/tjm/1422452802