On the p-rank strata of the moduli space of curves
by
Rachel Pries
Colorado State University
Coauthors: Jeff Achter

If X is a curve of genus g defined over an algebraically closed field k of characteristic p, then the p-rank of X is the integer f so that p^f is the number of p-torsion points on the Jacobian of X. We consider the p-rank stratification of the moduli space of curves and compute the integral monodromy of every component of the stratum of the moduli space of curves having genus g and p-rank f. As an application we show, for every g at least 3 and every f between 0 and g, that there is a k-curve with genus g and p-rank f whose Jacobian is absolutely simple.

Date received: April 17, 2008