UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ATTACHED TO HILBERT MODULAR FORMS MOD $p$ OF WEIGHT 1

@article{Dimitrov2018UNRAMIFIEDNESSOG,
  title={UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ATTACHED TO HILBERT MODULAR FORMS MOD \$p\$ OF WEIGHT 1},
  author={Mladen Dimitrov and Gabor Wiese},
  journal={Journal of the Institute of Mathematics of Jussieu},
  year={2018},
  volume={19},
  pages={281 - 306}
}
The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over $\overline{\mathbb{F}}_{p}$ 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… 
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