Duke Mathematical Journal

Companion forms over totally real fields, II

Toby Gee

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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

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

First available in Project Euclid: 21 December 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F33: Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50]


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

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