Th\'eorie locale du corps de classes et $(\varphi,\Gamma)$-modules Lubin-Tate

TL;DR

This paper connects the theory of Lubin-Tate $(, )$-modules to the determination of the maximal abelian extension of a finite extension of ${f Q}_p$, providing a new perspective in local class field theory.

Contribution

It demonstrates how Lubin-Tate $(, )$-modules can be used to deduce the maximal abelian extension of a local field.

Findings

Established a link between Lubin-Tate modules and class field theory

Provided a method to determine maximal abelian extensions using $(, )$-modules

Enhanced understanding of local class field theory through module theory

Abstract

We show how to deduce the determination of the maximal abelian extension of $F$, with $[F:{\mathbf Q}_p]<\infty$, from the theory of Lubin-Tate $(\varphi,\Gamma)$-modules.