Overconvergent Lubin-Tate $(\phi, \Gamma)$-modules for different uniformizers

TL;DR

This paper explores how overconvergent Lubin-Tate $(, abla)$-modules vary with different uniformizers in non-archimedean local fields, providing a functorial relationship and explicit analysis for 2-dimensional trianguline cases.

Contribution

It introduces a functor relating categories of overconvergent Lubin-Tate modules for different uniformizers and analyzes this functor explicitly for 2-dimensional trianguline representations.

Findings

Established a functor connecting modules for different uniformizers.

Provided explicit description for 2-dimensional trianguline representations.

Enhanced understanding of uniformizer dependence in $(, abla)$-modules.

Abstract

Let F be a non-archimedean local field. The construction of Lubin-Tate $(\phi_q, \Gamma)$-modules attached to p-adic representations of $G_F$ depends on the choice of a uniformizer of F. In this paper, we give a description of a functor which relates categories of overconvergent Lubin-Tate $(\phi_q, \Gamma)$-modules for different uniformizers. Further, we study this functor more explicitly for 2-dimensional trianguline representations.