Local-global problem for Drinfeld modules

Abstract

Let K be a function field and let (f) be a principal prime ideal of the ring A, which is a subring of K. Let phi: A --> K {tau} be a Drinfeld module. In this paper we consider the problem whether a point P in K which is a phi(f)-fold locally at each place v of K, i.e., for each v there is a Q in K_v such that phi(f).P = Q, is also a phi(f)-fold globally. We also discuss the same problem in the context of elliptic curves, where it is much simpler.