Wiese, Gabor[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

2015

No

[en] The main result of this article states that the Galois representation attached to a Hilbert modular eigenform over Fp of parallel weight one 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 one. The proof is based on the observation that parallel weight one forms in characteristic p embed into the ordinary part of parallel weight p in two different ways per place above p, namely via â€˜partialâ€™ Frobenius operators. These are defined in the article along with and based on Hecke operators Tp for p dividing p. The theorem is deduced from known local properties of the Galois representation attached to ordinary eigenforms in characteristic 0.