**Memoires de la Societe Mathematique de France**

Volume: 124;
2011;
194 pp;
Softcover

MSC: Primary 22;
**Print ISBN: 978-2-85629-311-9
Product Code: SMFMEM/124**

List Price: $45.00

AMS Member Price: $36.00

# Changement de Base et Induction Automorphe Pour \(\mathrm{GL}_{n}\) en Caractéristique non Nulle

Share this page
*Guy Henniart; Bertrand Lemaire*

A publication of the Société Mathématique de France

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.

#### Readership

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