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portada Cohomology of Drinfeld Modular Varieties (Cambridge Studies in Advanced Mathematics)
Type
Physical Book
Author
Publisher
Year
2009
Language
English
Pages
380
Format
Paperback
Dimensions
22.9 x 15.2 x 2.2 cm
Weight
0.55 kg.
ISBN
0521109906
ISBN13
9780521109901
Edition No.
1
Categories

Cohomology of Drinfeld Modular Varieties (Cambridge Studies in Advanced Mathematics)

Gerard Laumon (Author) · Laumon Gerard (Author) · Cambridge University Press · Paperback

Cohomology of Drinfeld Modular Varieties (Cambridge Studies in Advanced Mathematics) - Laumon, Gerard ; Gerard, Laumon ; Waldspurger, Jean Loup

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Synopsis "Cohomology of Drinfeld Modular Varieties (Cambridge Studies in Advanced Mathematics) "

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.

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