Unramifiedness of Galois representations attached to weight one Hilbert modular eigenforms mod p
Number Theory
2020-08-20 v4
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.
Keywords
Cite
@article{arxiv.1508.07722,
title = {Unramifiedness of Galois representations attached to weight one Hilbert modular eigenforms mod p},
author = {Mladen Dimitrov and Gabor Wiese},
journal= {arXiv preprint arXiv:1508.07722},
year = {2020}
}
Comments
24 pages; minor changes compared to previous version; accepted for publication in the Journal of the Institute of Mathematics of Jussieu