Serre weights for quaternion algebras

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.

Essentially final version, to appear in Compositio Mathematica. This version does not incorporate any minor changes (e.g. typographical changes) made in proof

References in corpus (3)

• On Serre's conjecture for mod l Galois representations over totally real fields
• On the weights of mod $p$ Hilbert modular forms
• Automorphic lifts of prescribed types

Cited by in corpus (3)

• Weight cycling and Serre-type conjectures for unitary groups
• Serre weights for locally reducible two-dimensional Galois representations
• On mod p non-abelian Lubin-Tate theory for GL_2(Q_p)