Approche non-invariante de la correspondance de Jacquet-Langlands: analyse g\'eom\'etrique

TL;DR

This paper introduces a geometric approach to the non-invariant transfer in the Jacquet-Langlands correspondence, utilizing trace formulas for Lie algebras and detailed conjugacy class analysis.

Contribution

It provides a new geometric proof of the trace formula comparison for general linear groups and their inner forms, emphasizing non-invariant transfer methods.

Findings

Description of conjugacy classes of inner forms of GL(n)

Explicit Haar measure computations

Development of non-invariant transfer techniques

Abstract

In this two-part series of articles, we present a new proof comparing the trace formula for a general linear group with that of one of its inner forms. Our methodology relies on the trace formula for Lie algebras, incorporating the notion of non-invariant transfer of test functions. In the appendix A, we provide a description of conjugacy classes of an inner form of a general linear group. In the appendix B, we provide explicit computations of Haar measures. This article focuses on the geometric side of the trace formula.