La formule des traces pour les rev\^etements de groupes r\'eductifs connexes. I. Le d\'eveloppement g\'eom\'etrique fin

TL;DR

This paper investigates the geometric side of the Arthur-Selberg trace formula for nonlinear covers of reductive groups, expressing it through weighted orbital integrals to advance towards an invariant trace formula.

Contribution

It provides a new expression of the geometric side of the trace formula for certain nonlinear covers, aiding the development of the invariant trace formula.

Findings

Expressed the geometric side in terms of weighted orbital integrals.

Applicable to Brylinski-Deligne covers.

Progress towards the invariant trace formula.

Abstract

We study the genuine part of the Arthur-Selberg trace formula for some nonlinear covers of connected reductive groups. As a first step towards the invariant trace formula, we express the geometric side in terms of weighted orbital integrals. In particular, our results apply to the covers constructed by Brylinksi and Deligne.