The Grothendieck-Katz Conjecture for certain locally symmetric varieties
  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 $g > 1.$ 
Benson Farb and Mark Kisin