Filtered modules corresponding to potentially semi-stable representations

TL;DR

This paper classifies filtered modules linked to two-dimensional potentially semi-stable p-adic Galois representations over p-adic fields, under specific assumptions on p and coefficients.

Contribution

It provides a classification of filtered modules associated with certain p-adic Galois representations, extending understanding under specific conditions.

Findings

Classification of filtered modules for two-dimensional potentially semi-stable representations

Results depend on p being odd and coefficients being sufficiently large

Advances the understanding of p-adic Galois representations in number theory

Abstract

We classify the filtered modules with coefficients corresponding to two-dimensional potentially semi-stable $p$-adic representations of the absolute Galois groups of $p$-adic fields under the assumptions that $p$ is odd and the coefficients are large enough.