  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. As an application, we get a stronger
result on the intersection of the theta divisor and torsion points on the
Jacobian variety for more general curves. New examples are discussed as well. A
key new ingredient is a map connecting the $p$-adic loop group and the formal
group.
