Toby Gee
Published 2004-08-12, updated 2010-09-03Version 3
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.
Comments: Appeared as Manuscripta Math. 125 (2008), no. 1, 1-41. This version does not incorporate any minor changes (e.g. typographical changes) made in proof
Mod $p$ Hilbert modular forms of parallel weight one: the ramified case
Converse theorems for Hilbert modular forms of higher level
Companion Forms in Parallel Weight One
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