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

TL;DR

This paper proves an analogue of Deligne's conjecture, establishing a Lefschetz trace formula for $p^n$-torsion étale cohomology over finite fields under specific conditions.

Contribution

It introduces a new version of Deligne's conjecture applicable to $p^n$-torsion étale cohomology and provides a proof under certain assumptions.

Findings

Established a Lefschetz trace formula for $p^n$-torsion étale cohomology.

Extended Deligne's conjecture to a new cohomological context.

Provided conditions under which the formula holds.

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 \'etale cohomology under certain conditions, where $p$ is the characteristic of the base field.