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Approche non-invariante de la correspondance de Jacquet-Langlands: analyse géométrique

Yan-Der Lu

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.

Approche non-invariante de la correspondance de Jacquet-Langlands: analyse géométrique

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.

Paper Structure

This paper contains 69 sections, 34 theorems, 298 equations.

Table of Contents

  1. Introduction
  2. Préface
  3. Résultats principaux
  4. Plan de l'article
  5. Préliminaires généraux
  6. Notations
  7. Objets relativement à F
  8. Objets relativement à G
  9. Objets relativement à un sous-groupe de Levi M ou à un sous-groupe parabolique P
  10. (G,M)-familles
  11. Généralités sur les groupes du type GL et notion de transfert des objets
  12. Orbites induites
  13. Espace de Schwartz-Bruhat
  14. Conventions
  15. Préliminaires locaux
  16. ...and 54 more sections

Key Result

Proposition 1.5

Il existe $\underline{S}$ un sous-ensemble fini de places, contenant les places archimédiennes, tel que pour tous $S\supseteq \underline{S}$ fini, $\mathcal{S}(\mathfrak{g}(F_S))\ni f_S\underset{}{\leftrightarrow} f_S^\ast \in \mathcal{S}(\mathfrak{g}^\ast(F_S))$ de type tenseur pur, $L'$ un sous-gr

Theorems & Definitions (90)

  • Proposition 1.5: proposition \ref{['prop:semi-localIOPcomp']}
  • Proposition 2.2
  • proof
  • proof
  • Proposition 2.5
  • proof
  • Proposition 2.6
  • proof
  • Proposition 2.8
  • proof
  • ...and 80 more