Toby Gee, David Savitt
Published 2009-09-07, updated 2010-08-31Version 2
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.
Comments: Essentially final version, to appear in Compositio Mathematica. This version does not incorporate any minor changes (e.g. typographical changes) made in proof
Serre weights for locally reducible two-dimensional Galois representations
Serre weights for mod p Hilbert modular forms: the totally ramified case
Galois action on knots I: Action of the absolute Galois group
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