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1 results

  • Hilbert modular forms and p-adic Hodge theory

  • Part of
  • Takeshi Saito
  • Journal:
    Compositio Mathematica / Volume 145 / Issue 5 / September 2009
    Published online by Cambridge University Press:
    21 September 2009, pp. 1081-1113
    Print publication:
    September 2009
    • Article
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  • For the p-adic Galois representation associated to a Hilbert modular form, Carayol has shown that, under a certain assumption, its restriction to the local Galois group at a finite place not dividing p is compatible with the local Langlands correspondence. Under the same assumption, we show that the same is true for the places dividing p, in the sense of p-adic Hodge theory, as is shown for an elliptic modular form. We also prove that the monodromy-weight conjecture holds for such representations.