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 phi over K. By E(K) we denote K together with the A-module structure induced on it by phi. For any principal prime ideal (a) subset of A, we study the question whether an element x is an element of E(K) which is an a-fold in E(K-nu) for every place nu of K, is an a-fold in E(K). In particular, we study the groupS(a, K) := ker E(K)/aE(K) --> Pi(nu) E(K-nu)/aE(K-nu)for Drinfeld modules of rank 2. We show that this finite group is trivial in many cases, but can become arbitrarily large. (C) 2003 Elsevier Inc. All rights reserved.