Asymptotique des nombres de Betti des vari\'et\'es arithm\'etiques

Abstract

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.