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Manuscripta Mathematica

, Volume 142, Issue 3–4, pp 513–524 | Cite as

On local Galois representations associated to ordinary Hilbert modular forms

  • Baskar Balasubramanyam
  • Eknath Ghate
  • Vinayak VatsalEmail author
Article

Abstract

Let F be a totally real field and p be an odd prime which splits completely in F. We show that a generic p-ordinary non-CM primitive Hilbert modular cuspidal eigenform over F of parallel weight two or more must have a locally non-split p-adic Galois representation, at at least one of the primes of F lying above p. This is proved under some technical assumptions on the global residual Galois representation. We also indicate how to extend our results to nearly ordinary families and forms of non-parallel weight.

Mathematics Subject Classification

11F41 11F80 11F85 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Baskar Balasubramanyam
    • 1
  • Eknath Ghate
    • 2
  • Vinayak Vatsal
    • 3
    Email author
  1. 1.Indian Institute of Science Education and ResearchPuneIndia
  2. 2.School of Mathematics, Tata Institute of Fundamental ResearchMumbaiIndia
  3. 3.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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