Le transfert singulier pour la formule des traces de Jacquet-Rallis

TL;DR

This paper establishes a transfer principle for the geometric terms in the Jacquet-Rallis relative trace formula, linking unitary and linear groups, with implications for the Gan-Gross-Prasad conjecture.

Contribution

It proves the transfer of all geometric terms between unitary and linear groups and shows their relation to local orbital integrals, advancing the understanding of trace formulas.

Findings

Transfer of geometric terms between unitary and linear groups established

All geometric terms are in the weak closure of local orbital integrals

Application to the Gan-Gross-Prasad conjecture for unitary groups

Abstract

The relative trace formula of Jacquet-Rallis (for unitary groups or general linear groups) is an identity between periods of automorphic representations and geometric distributions. In this paper, we prove the transfer between all geometric terms of unitary groups and those of linear groups. We also show that all geometric terms are in the weak closure of local regular semi-simple orbital integrals. We mention an application to the Gan-Gross-Prasad conjecture for unitary groups.