The p-torsion of curves in characteristic p
Rachel Pries
Consider the Jacobian of a curve X of genus g with p-rank f
defined over an algebraically closed field of characteristic p. The
p-torsion of this Jacobian is a group scheme and Kraft and Oort classified
the group schemes that can appear in this context. There are not many
results about which group schemes actually occur for such a curve X.
In this talk, I will state a conjecture about the group scheme which
occurs generically as the p-torsion of such a Jacobian. When f=g-2 and
f=g-3, I will prove the conjecture and give some other results. The method
involves computations on the boundary of the moduli space of curves and
might work more generally. I may also talk about results with Darren
Glass on the p-torsion of hyperelliptic curves and about results with Hui
June Zhu on the p-torsion of Artin-Schreier curves.