Book Titles On the Stabilization of the Trace Formula
From International Press
On the Stabilization of the Trace Formula
Edited by Laurent Clozel (Université Paris-Sud, Orsay) Michael Harris (Université Paris-Diderot Paris 7) Jean-Pierre Labesse (Université Aix-Marseille II) Bao-Châu Ngô (University of Chicago)
Publication Details
Hardcover. 527 pages.
ISBN: 978-1-57146-227-5
Release date: 28 June 2011
Publisher: International Press of Boston
2010 MSC: 11F70, 11F72, 11S37, 14D23, 22E35, 22E50.
Languages: English, French
List price: $100.00. Discounts may apply.
Full Description
This is the first volume of a projected series of two or three collections of mainly expository articles on the arithmetic theory of automorphic forms. The books are intended primarily for two groups of readers. The first group is interested in the structure of automorphic forms on reductive groups over number fields, and specifically in qualitative information about the multiplicities of automorphic representations. The second group is interested in the problem of classifying l–adic representations of Galois groups of number fields. Langlands' conjectures elaborate on the notion that these two problems overlap to a considerable degree. The goal of this series of books is to gather into one place much of the evidence that this is the case, and to present it clearly and succinctly enough so that both groups of readers are not only convinced by the evidence but can pass with minimal effort between the two points of view. More than a decade's worth of progress toward the stabilization of the Arthur-Selberg trace formula, culminating in Ngô Bau Châu's recent proof of the Fundamental Lemma, has made this series timely.
General Introduction: The stable trace formula, Shimura varieties, and arithmetic applications Michael Harris
Section I: Introduction to the stablization of the trace formula
An introduction to the stable trace formula Michael Harris
Introduction to endoscopy: Snowbird lectures, revised version, May 2010 Jean-Pierre Labesse
Section II: Endoscopy and transfer
Endoscopy for real reductive groups David Renard
Subsection II.B: The fundamental lemma and transfer
Le transfert lisse des intégrales orbitales, d'après Waldspurger Pierre-Henri Chaudouard
A propos du lemme fondamental tordu Jean-Loup Waldspurger
Subsection II.C: The fundamental lemma and the Hitchin fibration
Lemme Fondamental pour les algèbres de Lie, d'après Ngô Bao-Châu Jean-François Dat and Ngô Dac Tuan
Decomposition theorem and abelian fibration Ngô Bao-Châu
Endoscopie et changement de caractéristique, d'après Waldspurger Bertrand Lemaire
Transfer principle for the fundamental lemma Raf Cluckers, Thomas Hales, and François Loeser
Section III: Brief review of representation theory
Identités de caractères en la place archimédienne Laurent Clozel
Discrete series and characters of the component group Jeffrey Adams
Unramified representations of unitary groups Alberto Mínguez
Les facteurs de transfert pour les groupes unitaires Jean-Pierre Labesse
Section IV: Some examples of stable transfer
Introduction to Section IV Laurent Clozel, Michael Harris, and Jean-Pierre Labesse
Changement de base CM et séries discrètes Jean-Pierre Labesse
Appendice: Un erratum Laurent Clozel
Endoscopic transfer Laurent Clozel, Michael Harris, and Jean-Pierre Labesse
Construction of automorphic Galois representations, I Laurent Clozel, Michael Harris, and Jean-Pierre Labesse
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On the Stabilization of the Trace Formula
