Companion Forms Over Totally Real Fields

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Companion Forms Over Totally Real Fields

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Title: Companion Forms Over Totally Real Fields
Author: Gee, Toby
Citation: Gee, Toby. 2008. Companion forms over totally real fields. Manuscripta Mathematica 125(1): 1-41.
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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 ordinary at all primes dividing 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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