Cohomology of Drinfeld Modular Varieties, Part 2, Automorphic Forms, Trace Formulas and Langlands Correspondence (Cambridge Studies in Advanced Mathematics, Series Number 56) - Hardcover

Laumon, Gérard

Hardcover

ISBN 10: 0521470617 ISBN 13: 9780521470612

Publisher: Cambridge University Press, 1997

Synopsis

Cohomology of Drinfeld Modular Varieties aims to provide an introduction to this subject and to the Langlands correspondence for function fields. These varieties are the analogues for function fields of the Shimura varieties over number fields. The Langlands correspondence is a conjectured link between automorphic forms and Galois representations over a global field. By analogy with the number-theoretic case, one expects to establish the conjecture for function fields by studying the cohomology of Drinfeld modular varieties, which has been done by Drinfeld himself for the rank two case. This second volume is concerned with the ArthurSHSelberg trace formula, and to the proof in some cases of the Ramanujan-Petersson conjecture and the global Langlands conjecture for function fields. The author uses techniques that are extensions of those used to study Shimura varieties. Though the author considers only the simpler case of function rather than number fields, many important features of the number field case can be illustrated. Several appendices on background material keep the work reasonably self-contained. This book will be of much interest to all researchers in algebraic number theory and representation theory.

About this title

Book Description

Cohomology of Drinfeld Modular Varieties provides an introduction, in two volumes, both to this subject and to the Langlands correspondence for function fields. It is based on courses given by the author who, to keep the presentation as accessible as possible, considers the simpler case of function rather than number fields; nevertheless, many important features can still be illustrated. Several appendices on background material make this a self-contained book. It will be welcomed by workers in algebraic number theory and representation theory.

Review

"...these two volumes contain many results that are new and important....they are also the best source available for learning about the approacj to zeta functions via the theory of automorphic representations. They contain a wealth of information, theorems, and calculations, laid before the reader in Laumon's superb expository style....these two volumes are a welcome addition to the literature on automorphic representations and are highly recommended." Jonathan David Rogawski, Mathematical Reviews

Edition details

• Publisher: Cambridge University Press
• Publication date: 1997
• ISBN 10: 0521470617
• ISBN 13: 9780521470612
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 380