Mod $p$ Hilbert modular forms of parallel weight one: the ramified case
Number Theory
2017-11-07 v1
Abstract
We generalize the main result of arXiv:1206.6631 [math.NT] to all totally real fields. In other words, for prime, we prove (under a mild Taylor-Wiles hypothesis) that if a modular representation is unramified and -distinguished at all places above , then it arises from a mod Hilbert modular form of parallel weight one. This (mostly) resolves the weight one part of Serre's conjecture for totally real fields.
Cite
@article{arxiv.1711.01680,
title = {Mod $p$ Hilbert modular forms of parallel weight one: the ramified case},
author = {Payman L Kassaei},
journal= {arXiv preprint arXiv:1711.01680},
year = {2017}
}