  We investigate conformal actions of cocompact lattices in higher-rank simple
Lie groups on compact pseudo-Riemannian manifolds. Our main result gives a
general bound on the real-rank of the lattice, which was already known for the
action of the full Lie group by a result of Zimmer. When the real-rank is
maximal, we prove that the manifold is conformally flat. This indicates that a
global conclusion similar to that of anterior works of Bader, Nevo and Frances,
Zeghib in the case of a Lie group action might be obtained. We also give better
estimates for actions of cocompact lattices in exceptional groups. Our work is
strongly inspired by the recent breakthrough of Brown, Fisher and Hurtado on
Zimmer's conjecture.
