Torsion of algebraic groups and iterate extensions associated with Lubin-Tate formal groups

TL;DR

This paper investigates the finiteness of torsion points in commutative algebraic groups over p-adic fields, focusing on extensions related to Lubin-Tate formal groups and their implications in number theory.

Contribution

It establishes new finiteness results for torsion points over specific infinite algebraic extensions linked to Lubin-Tate formal groups, expanding understanding of p-adic Galois representations.

Findings

Finiteness of torsion points over abelian extensions with crystalline characters

Finiteness results for iterate extensions associated with Lubin-Tate formal groups

Connections established with Kummer theory in the context of formal groups

Abstract

We show finiteness results on torsion points of commutative algebraic groups over a $p$-adic field $K$ with values in various algebraic extensions $L/K$ of infinite degree. We mainly study the following cases: (1) $L$ is an abelian extension which is a splitting field of a crystalline character (such as a Lubin-Tate extension). (2) $L$ is a certain iterate extension of $K$ associated with Lubin-Tate formal groups, which is familiar with Kummer theory.