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Sur la cohomologie à supports compacts des variétés de Shimura pour GSp(4)$_{\bb Q}$

Published online by Cambridge University Press:  04 December 2007

GÉRARD LAUMON
GÉRARD LAUMON
Affiliation:
URA 752 du CNRS, Université Paris-Sud, Mathématiques, Bât. 425, F-91405 Orsay Cedex, France, Tél: 33 1 69 15 78 28, Fax: 33 1 69 15 60 19 e-mail: [email protected]
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Abstract

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In this paper we compute the cohomology with compact supports of a Siegel threefold as a virtual module over the product of the Galois group of$\bar{\bb Q}$ over ${\bb Q}$ and the Hecke algebra. We use a method which has been developed by Ihara, Langlands and Kottwitz: comparison of the Grothendieck—Lefschetz formula and the Arthur—Selberg trace formula.

Keywords

Shimura variety$\ell$-adic cohomologyautomorphic representation
Type
Research Article
Information
Compositio Mathematica , Volume 105 , Issue 3 , February 1997 , pp. 267 - 359
Copyright
© 1997 Kluwer Academic Publishers