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Cohomology of Drinfeld Modular Varieties: Series Number 41: Part 1: Geometry, Counting of Points and
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Cohomology of Drinfeld Modular Varieties: Series Number 41: Part 1: Geometry, Counting of Points and

Cohomology of Drinfeld Modular Varieties: Series Number 41: Part 1: Geometry, Counting of Points and

Gerard Laumon

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360 pages, parution le 08/12/2010
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Résumé

Originally published in 1995, Cohomology of Drinfeld Modular Varieties provided an introduction, in two volumes, to both the subject of the title and the Langlands correspondence for function fields. It is based on courses given by the author and will be welcomed by workers in number theory and representation theory.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.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-Poincare functions; 6. The Lefschetz numbers as sums of global elliptic orbital integrals; 7. Unramified principal series representations; 8. Euler-Poincare functions as pseudocoefficients of the Steinberg relation; Appendices.

Caractéristiques techniques

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Éditeur(s) Cambridge University Press
Auteur(s) Gerard Laumon
Parution 08/12/2010
Nb. de pages 360
EAN13 9780521172745

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