Torsion subgroups of Mordell-Weil groups of Fermat Jacobians, by Pavlos Tzermias

This paper has appeared in International Mathematics Research Notices (1998), no. 7, pages 359-369, and so the dvi version has been removed. Let p be a fixed prime, such that p > 7. Let F and J denote the Fermat curve of degree p and its Jacobian, respectively. Finally, let K denote the cyclotomic extension of Q generated by a primitive p-th root of 1. In this paper, we compute the precise structure of the torsion parts of the Mordell-Weil groups of J over all proper subfields of K. We show that the above torsion groups are all contained in the cuspidal divisor class group of F, which was studied by Rohrlich. In particular, we show that every Q-rational torsion point on J is the equivalence class of a divisor of degree 0 on F supported on the three Q-rational points on F.

Pavlos Tzermias <>