Inventiones mathematicae

, Volume 185, Issue 1, pp 1–16

Even Galois representations and the Fontaine–Mazur conjecture

Article

DOI: 10.1007/s00222-010-0297-0

Cite this article as:
Calegari, F. Invent. math. (2011) 185: 1. doi:10.1007/s00222-010-0297-0

Abstract

We prove, under mild hypotheses, that there are no irreducible two-dimensional ordinary even Galois representations of \(\mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q})\) with distinct Hodge–Tate weights. This is in accordance with the Fontaine–Mazur conjecture. If K/Q is an imaginary quadratic field, we also prove (again, under certain hypotheses) that \(\mathrm{Gal}(\overline{\mathbf{Q}}/K)\) does not admit irreducible two-dimensional ordinary Galois representations of non-parallel weight.

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA