Companion Forms Over Totally Real Fields, II

Abstract

We prove a companion forms theorem for mod l Hilbert modular forms. This work generalises results of Gross and Coleman--Voloch for modular forms over Q, and gives a new proof of their results in many cases. The methods used are completely different to previous work in this area, and rely on modularity lifting theorems and the general theory of deformations of Galois representations.

8 pages. Essentially final version, appeared in Duke Math. Journal 136 (2007), no. 2. This version does not incorporate any minor changes (e.g. typographical changes) made in proof