Companion forms over totally real fields

Details Companion forms over totally real fields Companion forms over totally real fields

2004-08-12

arxiv.org/abs/math/0408167v3

Mathematics

Number Theory

Appeared as Manuscripta Math. 125 (2008), no. 1, 1-41. This version does not incorporate any minor changes (e.g. typographical

Scientific paper

We show that if F is a totally real field in which p splits completely and f
is a mod p Hilbert modular form with parallel weight 2ordinary at p and has tamely ramified Galois representation at all primes
dividing p, then there is a "companion form" of parallel weight k':=p+1-k. This
work generalises results of Gross and Coleman-Voloch for modular forms over Q.

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