The Hodge conjecture and arithmetic quotients of complex balls

Nicolas Bergeron, John Millson, Colette Moeglin

Let $S$ be a closed Shimura variety uniformized by the complex $n$-ball. The Hodge conjecture predicts that every Hodge class in $H^{2k} (S, \Q)$, $k=0,\dots ,n$, is algebraic. W…