Torsion points of Drinfeld modules over large algebraic extensions of finitely generated function fields

TL;DR

This paper extends results about torsion points from elliptic curves to Drinfeld modules over large algebraic extensions of finitely generated function fields, revealing similar Galois-theoretic properties.

Contribution

It provides new theorems on torsion points of Drinfeld modules over fixed fields defined by finitely many Galois elements, paralleling prior elliptic curve results.

Findings

Results analogous to Geyer and Jarden for Drinfeld modules

Torsion points behavior over large algebraic extensions

Galois group fixed field torsion properties

Abstract

Geyer and Jarden proved several results for torsion points of elliptic curves defined over the fixed field by finitely many elements in the absolute Galois group of a finitely generated field over the prime field in its algebraic closure. As an analogue of these results, this paper studies torsion points of Drinfeld modules defined over the fixed field by finitely many elements in the absolute Galois group of a finitely generated function field in its algebraic closure. We prove some results which are similar to those of Geyer and Jarden.