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arXiv · 1508.07722

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

Mladen Dimitrov·Gabor Wiese
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Abstract

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.

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Mladen Dimitrov, Gabor Wiese. 2015-08-31. Unramifiedness of Galois representations attached to weight one Hilbert modular eigenforms mod p. https://doi.org/10.1017/s1474748018000026

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