On Field Generated by Division Points of Several Formal Groups

TL;DR

This paper investigates the fields generated by division points of multiple formal groups of the same height, showing they are equivalent to the field generated by a single formal group's division points after a finite unramified extension.

Contribution

It proves that under certain conditions, the field generated by division points of several formal groups equals that of one formal group after a finite unramified extension.

Findings

Field generated by multiple formal groups' division points equals that of one group after extension

Results are based on hypotheses related to formal groups of same height

Extends implicit results from previous thesis work

Abstract

In this article we prove some interesting results on field generated by division points of several formal groups of same height, already implicit in the treatment in appendix-A of my M.Sc thesis (Points of Small Height in Certain Nonabelian Extensions). More precisely, under suitable hypothesis we show that the field generated by the division points of several formal groups is equal to the field generated by division points of an individual formal group among them, after a fixed finite unramified extension of base field.