English

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.

Keywords

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

R2 v1 2026-06-21T13:43:31.026Z