A note on Fontaine theory using different Lubin-Tate groups

TL;DR

This paper explores Fontaine's theory by comparing $(,)$ modules linked to Galois representations through various Lubin-Tate groups, highlighting how different choices influence the associated modules.

Contribution

It introduces a comparison framework for Fontaine's $(,)$ modules using different Lubin-Tate groups, expanding understanding of their role in Galois representations.

Findings

Different Lubin-Tate groups yield distinct $(,)$ modules.

The comparison clarifies the impact of Lubin-Tate group choice on Galois representation theory.

The results provide new insights into the structure of Fontaine's modules in local fields.

Abstract

Using different Lubin-Tate groups, we compare $(\phi, \Gamma)$ modules associated to a Galois representation via Fontaine's theory.