Sur le spectre et la topologie des vari\'et\'es hyperboliques de   congruence : les cas complexe et quaternionien
  Building on results of Arthur and Mok, we extend to (finite volume) complex and quaternionic hyperbolic manifolds the results of arXiv:1004.1085. For the spherical spectrum our results are optimal. Finally, as an application we prove a Lefschetz property for the restriction map between arithmetic quotients of complex balls. This generalizes a recent theorem of Arvind Nair and gives an optimal version of it. 
Nicolas Bergeron and Laurent Clozel
math.NT math.GT