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Classification of two-dimensional split trianguline representations of p-adic fields

Part of: Algebraic number theory: local and $p$-adic fields Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  01 July 2009

Kentaro Nakamura
Kentaro Nakamura*
Affiliation:
Department of Mathematical Sciences, University of Tokyo, 153-8914, Tokyo, Japan (email: kentarou@ms.u-tokyo.ac.jp)
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Abstract

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The aim of this article is to classify two-dimensional split trianguline representations of p-adic fields. This is a generalization of a result of Colmez who classified two-dimensional split trianguline representations of for p≠2 by using (φ,Γ)-modules over a Robba ring. In this article, for any prime p and for any p-adic field K, we classify two-dimensional split trianguline representations of using B-pairs as defined by Berger.

Keywords

p-adic Hodge theorytrianguline representationsB-pairs

MSC classification

Secondary: 11F80: Galois representations 11F85: $p$-adic theory, local fields 11S25: Galois cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 4 , July 2009 , pp. 865 - 914
Copyright
Copyright © Foundation Compositio Mathematica 2009

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