Reference : Unramifiedness of Galois representations attached to weight one Hilbert modular eigen...
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Physical, chemical, mathematical & earth Sciences : Mathematics
Unramifiedness of Galois representations attached to weight one Hilbert modular eigenforms mod p
Dimitrov, Mladen []
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
In press
Journal of the Institute of Mathematics of Jussieu
Cambridge University Press
United Kingdom
[en] 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.
MSC: 11F80 (primary); 11F41, 11F33
Keywords: Hilbert modular forms modulo p, weight one, Galois representations

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