Cohomology of Drinfeld Modular Varieties, Part 2, Automorphic Forms, Trace Formulas and Langlands Correspondence

Jean Loup Waldspurger Gerard Laumon Laumon Gerard

ISBN 10: 0521109906 / ISBN 13: 9780521109901

Published by Cambridge University Press CUP, 2009

About this Item

pp. 380.

Seller Inventory # 26530433

Bibliographic Details

• Title: Cohomology of Drinfeld Modular Varieties, Part 2, Automorphic Forms, Trace Formulas and Langlands Correspondence
• Publisher: Cambridge University Press CUP
• Publication Date: 2009
• Language: English
• ISBN 10: 0521109906
• ISBN 13: 9780521109901
• Binding: Soft cover
• Condition: New

About this title

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.

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.