Duke Mathematical Journal

Asymptotique des nombres de Betti des variétés arithmétiques

Mathieu Cossutta

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Résumé

Nous étudions la question de la croissance des nombres de Betti de certaines variétés arithmétiques dans des revêtements de congruence. Plus précisement nos résultats portent sur les variétés de Siegel et les variétés associées à des groupes orthogonaux. Nous expliquons comment un théorème de Waldspurger permet de majorer et de minorer ces nombres. Les résultats obtenus vont dans le sens de conjectures de Sarnak et Xue [SX].

Abstract

We study the question of the growth of Betti numbers of certain arithmetic varieties in a tower of congruence coverings. In fact, our results are about Siegel varieties and varieties associated to orthogonal groups. We explain how a theorem of Waldspurger can be used to obtain lower and upper bounds. Our results are in the direction of conjectures made by Sarnak and Xue [SX]

Article information

Source
Duke Math. J., Volume 150, Number 3 (2009), 443-488.

Dates
First available in Project Euclid: 27 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1259332506

Digital Object Identifier
doi:10.1215/00127094-2009-057

Mathematical Reviews number (MathSciNet)
MR2582102

Zentralblatt MATH identifier
1263.11060

Subjects
Primary: 11F75: Cohomology of arithmetic groups
Secondary: 11F27: Theta series; Weil representation; theta correspondences 11F70: Representation-theoretic methods; automorphic representations over local and global fields

Citation

Cossutta, Mathieu. Asymptotique des nombres de Betti des variétés arithmétiques. Duke Math. J. 150 (2009), no. 3, 443--488. doi:10.1215/00127094-2009-057. https://projecteuclid.org/euclid.dmj/1259332506


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