## Duke Mathematical Journal

### Companion forms over totally real fields, II

Toby Gee

#### Abstract

We prove a companion forms theorem for mod $l$ Hilbert modular forms. This work generalises results of Gross [Gr] and Coleman and Voloch [CV] for modular forms over ${\mathbb Q}$ 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

#### Article information

Source
Duke Math. J. Volume 136, Number 2 (2007), 275-284.

Dates
First available in Project Euclid: 21 December 2006

https://projecteuclid.org/euclid.dmj/1166711370

Digital Object Identifier
doi:10.1215/S0012-7094-07-13622-6

Mathematical Reviews number (MathSciNet)
MR2286631

Zentralblatt MATH identifier
1121.11039

#### Citation

Gee, Toby. Companion forms over totally real fields, II. Duke Math. J. 136 (2007), no. 2, 275--284. doi:10.1215/S0012-7094-07-13622-6. https://projecteuclid.org/euclid.dmj/1166711370.

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