Serre weights for quaternion algebras

Mathematics – Number Theory

Scientific paper

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

Scientific paper

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.

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