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Hilbert modular forms and p-adic Hodge theory

Part of: Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  21 September 2009

Takeshi Saito
Takeshi Saito*
Affiliation:
Department of Mathematical Sciences, University of Tokyo, Tokyo 153-8914, Japan (email: t-saito@ms.u-tokyo.ac.jp)
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Abstract

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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.

Keywords

Hilbert modular formsGalois representationsLanglands correspondencesp-adic Hodge theory

MSC classification

Secondary: 11F80: Galois representations 11F41: Automorphic forms on $(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11G18: Arithmetic aspects of modular and Shimura varieties 14G35: Modular and Shimura varieties
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 5 , September 2009 , pp. 1081 - 1113
Copyright
Copyright © Foundation Compositio Mathematica 2009

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