Asymptotique des nombres de Betti des variétés arithmétiques

Mathieu Cossutta (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

We study the question of the growth of Betti numbers of certain arithmetic varieties in 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 bound. Our results are in the direction of conjectures made by Sarnak and Xue.

Domaines: Théorie des nombres [math.NT]

Mathieu Cossutta. Asymptotique des nombres de Betti des variétés arithmétiques. 2008. ⟨hal-00290583⟩