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Changement de Base et Induction Automorphe Pour \(\mathrm{GL}_n\) en Caractéristique non Nulle
Guy Henniart, Université Paris-Sud, Orsay, France, and Bertrand Lemaire, Université Aix-Marseille II, France
A publication of the Société Mathématique de France.
Mémoires de la Société Mathématique de France
2011; 194 pp; softcover
Number: 124
ISBN-10: 2-85629-311-5
ISBN-13: 978-2-85629-311-9
List Price: US$45
Member Price: US$36
Order Code: SMFMEM/124
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Let \(E/F\) be a finite cyclic extension of local or global fields, of degree \(d\). The theory of base change from \({\rm GL}_n(F)\) to \({\rm GL}_n(E)\) and the theory of automorphic induction from \({\rm GL}_m(E)\) to \({\rm GL}_{md}(F)\) are two instances of Langlands' functoriality principle: when \(F\) is local, they correspond respectively to restriction to \(E\) of representations of the Weil-Deligne group of \(F\), and induction to \(F\) of representations of the Weil-Deligne group of \(E\). If \(F\) is a finite extension of a \(p\)-adic field \(\mathbb {Q}_p\), these theories were established long ago (Arthur-Clozel, Henniart-Herb).

In this memoir the authors extend them to the case where \(F\) is a non-Archimedean locally compact field of positive characteristic. They also prove, for a global functions field \(F\), that these two local theories are compatible with the global maps of base change and automorphic induction deduced, via the Langlands correspondence proved by Lafforgue, from restriction and induction of global Galois representations.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.


Graduate students and research mathematicians interested in algebra and algebraic geometry.

Table of Contents

  • Introduction
  • Le lemme fondamental pour le changement de base pour \(\mathrm{GL}_n\) sur un corps local de caractéristique non nulle
  • Sur le changement de base local pour \(\mathrm{GL}_n\)
  • Formules de caractéres pour l'induction automorphe, II
  • Sur le changement de base et l'induction automorphe pour les corps de fonctions
  • Bibliographie
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