A p-adic family of dihedral (phi,Gamma)-modules

TL;DR

This paper constructs an explicit p-adic family of dihedral (phi,Gamma)-modules, detailing their matrices and identifying which are trianguline, advancing understanding of p-adic Galois representations.

Contribution

It explicitly constructs a p-adic family of dihedral (phi,Gamma)-modules and determines their trianguline properties, providing concrete matrices and classifications.

Findings

Explicit matrices for phi and Gamma actions are provided.

Identification of trianguline modules within the family.

Enhanced understanding of dihedral p-adic Galois representations.

Abstract

The goal of this article is to construct explicitly a p-adic family of representations (which are dihedral representations), to construct their associated (phi,Gamma)-modules by writing down explicit matrices for phi and for the action of Gamma, and finally to determine which of these are trianguline.