Local–global problem for Drinfeld modules

Let K be a function field with an A-algebra structure. The ring A arises in the definition of the Drinfeld module φ over K. By E(K) we denote K together with the A-module structure induced on it by φ. For any principal prime ideal (a) A, we study the question whether an element x E(K) which is an a-fold in E(Kν) for every place ν of K, is an a-fold in E(K). In particular, we study the group for Drinfeld modules of rank 2. We show that this finite group is trivial in many cases, but can become arbitrarily large.