The cuspidal torsion packet on the Fermat curve, by Robert F. Coleman, Akio Tamagawa and Pavlos Tzermias

This paper has appeared in J. Reine Angew. Math. 496 (1998), 73-81, and so the dvi version has been removed. We consider the Fermat curves of degree at least 4. For such a curve, we fix the Albanese embedding into its Jacobian, by taking a cusp (i.e. a point for which one of the projective coordinates vanishes) as a base point. The cuspidal torsion packet on the curve is defined as the set of points on the curve whose image under this embedding is a torsion point on the Jacobian. In this paper, we prove that the cuspidal torsion packet on such a curve is the set of cusps.

Robert F. Coleman, Akio Tamagawa and Pavlos Tzermias <coleman@math.berkeley.edu,tamagawa@kurims.kyoto-u.ac.jp,tzermias@crm.es>