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  1. Home
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  3. Cohomology of Drinfeld Modular Varieties
  • Cited by 23
  • Part 1: Geometry, Counting of Points and Local Harmonic Analysis
  • Gérard Laumon, Université de Paris XI
Publisher:
Cambridge University Press
Online publication date:
May 2010
Print publication year:
1995
Online ISBN:
9780511666162
DOI:
https://doi.org/10.1017/CBO9780511666162
Subjects:
Mathematics (general), Mathematics, Number Theory
Series:
Cambridge Studies in Advanced Mathematics (41)
Information

Book description

Originally published in 1995, Cohomology of Drinfeld Modular Varieties aimed to provide 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. The present volume is devoted to the geometry of these varieties, and to the local harmonic analysis needed to compute their cohomology. 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.

Reviews

Review of the hardback:‘This is a very impressive achievement.’

H.J. Baues Source: Mathematika

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