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Cohomology of Drinfeld Modular Varieties

Part 1. Geometry, Counting of Points and Local Harmonic Analysis

$65.99 (C)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: December 2010
  • availability: Available
  • format: Paperback
  • isbn: 9780521172745

$ 65.99 (C)

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About the Authors
  • Cohomology of Drinfeld Modular Varieties aims to provide an introduction to both the subject of the title and the Langlands correspondence for function fields. These varieties are the analogs for function fields of Shimura varieties over number fields. This present volume is devoted to the geometry of these varieties and to the local harmonic analysis needed to compute their cohomology. To keep the presentation as accessible as possible, the author considers the simpler case of function rather than number fields; nevertheless, many important features can still be illustrated. It will be welcomed by workers in number theory and representation theory.

    • Includes the Langlands correspondence
    • Author is well placed to write
    • Based on graduate courses in USA
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    Reviews & endorsements

    "...these two volumes contain many results that are new and important....they are also the best source available for learning about the approacj to zeta functions via the theory of automorphic representations. They contain a wealth of information, theorems, and calculations, laid before the reader in Laumon's superb expository style....these two volumes are a welcome addition to the literature on automorphic representations and are highly recommended." Jonathan David Rogawski, Mathematical Reviews

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    Product details

    • Date Published: December 2010
    • format: Paperback
    • isbn: 9780521172745
    • length: 360 pages
    • dimensions: 229 x 152 x 20 mm
    • weight: 0.53kg
    • availability: Available
  • Table of Contents

    1. Construction of Drinfeld modular varieties
    2. Drinfeld A-modules
    3. The Lefschetz numbers of Hecke operators
    4. The fundamental lemma
    5. Very cuspidal Euler–Poincaré functions
    6. The Lefschetz numbers as sums of global elliptic orbital integrals
    7. Unramified principal series representations
    8. Euler-Poincaré functions as pseudocoefficients of the Steinberg relation

  • Author

    Gérard Laumon, Université de Paris XI

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