**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

Individual Member Price: $36.00

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

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*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.