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. © 2009 Foundation Compositio Mathematica.
CITATION STYLE
Saito, T. (2009). Hilbert modular forms and p-adic Hodge theory. Compositio Mathematica, 145(5), 1081–1113. https://doi.org/10.1112/S0010437X09004175
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