# Companion Forms Over Totally Real Fields

 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. Full Text & Related Files: Gee - Companion forms.pdf (408.7Kb; PDF) 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 $$Q$$. Published Version: http://dx.doi.org/10.1007/s00229-007-0128-9 Other Sources: http://www.math.harvard.edu/~tgee/ Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:2943908 Downloads of this work:

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