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

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

EnglishPaperback / softbackPrint on demand
Laumon, Gérard
Cambridge University Press
EAN: 9780521109901
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Detailed information

Cohomology of Drinfeld Modular Varieties provides an introduction, in two volumes, both 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 Arthur-Selberg trace formula, and with the proof in some cases of the Rmamanujan-Petersson conjecture and the global Langlands conjecture for function fields. It is based on graduate courses taught by the author, who uses techniques which 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. It is the first book on this subject and will be of much interest to all researchers in algebraic number theory and representation theory.
EAN 9780521109901
ISBN 0521109906
Binding Paperback / softback
Publisher Cambridge University Press
Publication date April 30, 2009
Pages 380
Language English
Dimensions 229 x 152 x 21
Country United Kingdom
Authors Laumon, Gerard
Illustrations Worked examples or Exercises
Series Cambridge Studies in Advanced Mathematics
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