On the torsion of Drinfeld modules of rank two

TL;DR

This paper investigates the torsion points on rank two Drinfeld modules over function fields, leading to a conjecture that supports Poonen's uniform boundedness conjecture in this context.

Contribution

It introduces a conjecture characterizing torsion of rank two Drinfeld modules over f_2(T), connecting it to Poonen's uniform boundedness conjecture.

Findings

Derives a conjecture describing torsion points on Drinfeld modules of rank two.

Shows the conjecture implies Poonen's uniform boundedness conjecture in this case.

Analyzes rational points on Drinfeld modular curves over function fields.

Abstract

We study rational points and torsion points on Drinfeld modular curves defined over rational function fields. As a consequence we derive a conjecture of Schweizer describing completely the torsion of Drinfeld modules of rank two over $\Bbb F_2(T)$ implying Poonen's uniform boundedness conjecture in this particular case.