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

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

2008-01-08

arxiv.org/abs/0801.1230v2

Mathematics

Number Theory

1st version 47pages, 2nd version 52pages

Scientific paper

The aim of this paper 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 $\mathrm{Gal}(\bar{\mathbb{Q}}_p/\mathbb{Q}_p)$ by using $(\phi,\Gamma)$-modules over Robba ring. In this paper, we classify two dimensional split trianguline representations of $\mathrm{Gal}(\bar{K}/K)$ for general $p$-adic field $K$ by using $B$-pairs defined by Berger.

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