On the uniform boundedness conjecture for Drinfeld modules

 In analogy with the famous theorems of Mazur and Merel on the torsion subgroups of elliptic curves, one can formulate similar conjectures for the torsion points of Drinfeld modules. We prove some partial results for rank 2 Drinfeld 𝔽 _q T]-modules, for example the uniform boundedness of the 𝔭-primary torsion. Received: 22 May 2001; in final form 4 September 2002 / Published online: 1 April 2003