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Companion forms over totally real fields

Toby Gee
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Abstract

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 2<k<p, which is totally ordinary 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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Toby Gee. 2004-08-12. Companion forms over totally real fields. https://arxiv.org/abs/math/0408167

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