Noncommutative L-functions for varieties over finite fields

TL;DR

This paper extends the Grothendieck trace formula to L-functions associated with noncommutative adic sheaves on varieties over finite fields, broadening the scope of trace formula applications.

Contribution

It introduces a Grothendieck trace formula for L-functions of noncommutative adic sheaves, a novel generalization in the study of arithmetic geometry.

Findings

Established a trace formula for noncommutative sheaves

Extended L-function analysis beyond commutative cases

Provided new tools for arithmetic geometry research

Abstract

In this article we prove a Grothendieck trace formula for L-functions of not necessarily commutative adic sheaves.