Cohomology of Drinfeld Modular Varieties, Part 2, Automorphic Forms, Trace Formulas and Langlands Correspondence (Paperback) (ISBN-13: 9780521109901)

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.

Author: Gerard Laumon, Laumon Gerard, Jean Loup Waldspurger
ISBN-10: 0521109906
ISBN-13: 9780521109901
Publisher: Cambridge University Press
Language: English
Published: 04/30/2009
Pages: 380
Format: Paperback
Weight: 1.22lbs
Size: 9.00h x 6.00w x 0.85d