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  • Mladen Dimitrov (a1) and Gabor Wiese (a2)

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 in two different ways per prime dividing  $p$ , namely via ‘partial’ Frobenius operators.

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Journal of the Institute of Mathematics of Jussieu
  • ISSN: 1474-7480
  • EISSN: 1475-3030
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