Journal of the Institute of Mathematics of Jussieu ( IF 1.400 ) Pub Date : 2018-04-23 , DOI: 10.1017/s1474748018000026
Mladen Dimitrov; Gabor Wiese

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.

down
wechat
bug