Rank 3 filtered $(\varphi,N)$-modules

TL;DR

This paper provides a classification of 3-dimensional semistable Frobenius-semisimple Galois representations over p-adic fields, advancing understanding of their structure and properties.

Contribution

It introduces a comprehensive classification of rank 3 filtered $(, )$-modules, specifically for semistable Frobenius-semisimple representations.

Findings

Complete classification of 3-dimensional semistable $(, )$-modules.

Identification of key invariants and structures in these modules.

Framework for analyzing similar representations in number theory.

Abstract

We classify 3-dimensional semistable Frob-semisimple representations of $G_{\mathbb{Q}_{p^{f}}}.$