Serre weights for quaternion algebras
Number Theory
2019-02-20 v2
Abstract
We study the possible weights of an irreducible two-dimensional mod p representation of the absolute Galois group of F which is modular in the sense of that it comes from an automorphic form on a definite quaternion algebra with centre F which is ramified at all places dividing p, where F is a totally real field. In most cases we determine the precise list of possible weights; in the remaining cases we determine the possible weights up to a short and explicit list of exceptions.
Cite
@article{arxiv.0909.1278,
title = {Serre weights for quaternion algebras},
author = {Toby Gee and David Savitt},
journal= {arXiv preprint arXiv:0909.1278},
year = {2019}
}
Comments
Essentially final version, to appear in Compositio Mathematica. This version does not incorporate any minor changes (e.g. typographical changes) made in proof