Stefano Morra

Serre weights for three-dimensional ordinary Galois representations: SERRE WEIGHTS FOR THREE-DIMENSIONAL ORDINARY GALOIS REPRESENTATIONS

Let F/Q be a CM field where p splits completely and let r : Gal(Q/F ) → GL3(Fp) be a Galois representation whose restriction to Gal(Qp/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.