1210.5838 (Shinichi Kobayashi et al.)

Torsion points on Jacobian varieties via Anderson's p-adic soliton
theory    [PDF]

Shinichi Kobayashi, Takao Yamazaki

Anderson introduced a $p$-adic version of soliton theory. He then applied it to the Jacobian variety of a cyclic quotient of a Fermat curve and showed that torsion points of certain prime order lay outside of the theta divisor. In this paper, we evolve his theory further by using the Artin-Hasse exponential and Hasse-Witt matrix. As an application, we get a stronger result on the intersection of the theta divisor and torsion points on the Jacobian variety of a more general class of curves.

View original: http://arxiv.org/abs/1210.5838