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Serre weights for quaternion algebras

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  09 February 2011

Toby Gee  and
David Savitt
Toby Gee
Affiliation:
Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA 02138, USA (email: tgee@math.harvard.edu)
David Savitt
Affiliation:
Department of Mathematics, University of Arizona, 617 N. Santa Rita Avenue, Tucson, AZ 85712, USA (email: savitt@math.arizona.edu)
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Abstract

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We study the possible weights of an irreducible two-dimensional mod p representation of ${\rm Gal}(\overline {F}/F)$ which is modular in the sense 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

Galois representationsSerre weightsquaternion algebrasBreuil modules

MSC classification

Secondary: 11F33: Congruences for modular and $p$-adic modular forms 11F80: Galois representations

Information

Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 4 , July 2011 , pp. 1059 - 1086
Copyright
Copyright © Foundation Compositio Mathematica 2011

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