Arithmeticity vs. nonlinearity for irreducible lattices

Abstract. We establish an arithmeticity vs. non-linearity alternative for irreducible lat-tices in suitable product groups, for instance products of topologically simple groups. This applies notably to a (large class of) Kac-Moody groups. The alternative relies heavily on the superrigidity theorem we propose in [Md], since we follow Margulis ’ reduction of arith-meticity to superrigidity. 1