Serre weights for three-dimensional ordinary Galois representations

Abstract

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