SERRE WEIGHTS FOR THREE-DIMENSIONAL ORDINARY GALOIS REPRESENTATIONS

International audience; Let F/Q be a CM field where p splits completely and let r : Gal(Q/F) → GL 3 (Fp) be a Galois representation whose restriction to Gal(Q p /Fw) is ordinary and strongly generic for all places w above p. In this paper we specify the set of Serre weights in which r can be modular. To this aim, we develop a technique in integral p-adic Hodge theory to describe extensions of rank-one Breuil modules.