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
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
of degree 0 on F supported on the three Q-rational points on F.
Pavlos Tzermias <email@example.com>