Some properties of non-positively curved lattices

We announce results on the structure of CAT(0) groups, CAT(0) lattices and of the underlying spaces. Our statements rely notably on a general study of the full isometry groups of proper CAT(0) spaces. Classical statements about Hadamard manifolds are established for singular spaces; new arithmeticity and rigidity statements are obtained. To cite this article: P.-E. Caprace, N. Monod, C. R. Acad. Sci. Paris, Ser. I 346 (2008).