On the torsion of Drinfeld modules of rank two

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 ${\mathbb{F}}_2(T)$ implying Poonen's uniform boundedness conjecture in this particular case.

revised version, 44 pages, to appear in Crelle