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

Abstract

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 $(\varphi ,\Gamma )$-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.

1st version 47pages, 2nd version 52pages

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Cited by in corpus (14)

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• Paraboline variation of $p$-adic families of $(\phi ,\Gamma )$-modules
• Trianguline representations
• Représentations galoisiennes automorphes et conséquences arithmétiques des conjectures de Langlands et Arthur
• On admissible tensor products in $p$-adic Hodge theory
• Higher $\mathcal{L}$-invariants for ${\mathrm{GL}}_3({\mathbb{Q}}_p)$ and local-global compatibility
• Smoothness and Classicality on eigenvarieties
• On triangulable tensor products of B-pairs and trianguline representations
• Companion points on the eigenvariety with non-regular weights
• Deformations of trianguline B-pairs
• A generalization of Colmez-Greenberg-Stevens formula