Everett W. Howe: Optimal quotients and surjections of Mordell–Weil groups, J. Number Theory 166 (2016) 85–92.

Offical version here. Preprint version: arXiv:1505.07141 [math.NT].

Answering a question of Ed Schaefer, we show that if J is the Jacobian of a curve C over a number field, if s is an automorphism of J coming from an automorphism of C, and if u lies in the subring Z[s] of End J and has connected kernel, then it is not necessarily the case that u gives a surjective map from the Mordell–Weil group of J to the Mordell–Weil group of its image.