Unramifiedness of Galois representations attached to weight one Hilbert modular eigenforms mod p

The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over F_p^bar of parallel weight 1 and level prime to p is unramified above p. This includes the important case of eigenforms that do not lift to Hilbert modular forms in characterist...

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Bibliographic Details
Published in:arXiv.org 2017-11
Main Authors: Dimitrov, Mladen, Wiese, Gabor
Format: Article
Language:English
Subjects:
Representations
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Online Access:Get full text
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Summary:The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over F_p^bar of parallel weight 1 and level prime to p is unramified above p. This includes the important case of eigenforms that do not lift to Hilbert modular forms in characteristic 0 of parallel weight 1. The proof is based on the observation that parallel weight 1 forms in characteristic p embed into the ordinary part of parallel weight p forms in two different ways per prime dividing p, namely via `partial' Frobenius operators.
ISSN:2331-8422
DOI:10.48550/arxiv.1508.07722