Deligne's conjecture on the Lefschetz trace formula for $p^n$-torsion étale cohomology

Abstract

Deligne's conjecture is the Lefschetz trace formula for correspondences defined over a finite field. In this paper, we prove an analogous statement of Deligne's conjecture with respect to $p^n$-torsion étale cohomology under certain conditions, where $p$ is the characteristic of the base field.