http://arxiv.org/abs/0807.1152

The Grothendieck-Katz Conjecture for certain locally symmetric varieties
Benson Farb, Mark Kisin
(Submitted on 8 Jul 2008)

Using Margulis's results on lattices in semisimple Lie groups, we prove the Grothendieck-Katz $p$-Curvature Conjecture for certain locally symmetric varieties, including the moduli space of abelian varieties ${\cal A}_g$ when $g > 1.$