  We show that the module of rational points on an abelian t-module E is
canonically isomorphic with the module Ext^1(M_E, K[t]) of extensions of the
trivial t-motif K[t] by the t-motif M_E associated with E. This generalizes
prior results of Anderson and Thakur, Papanikolas and Ramachandran, and Woo.
  In case E is uniformizable then we show that this extension module is
canonically isomorphic with the corresponding extension module of Pink-Hodge
structures.
  This situation is formally very similar to Deligne's theory of 1-motifs and
we have tried to build up the theory in a way that makes this analogy as clear
as possible.
