Jeff Achter, Rachel Pries
Published 2007-07-13, updated 2008-05-28Version 2
We compute the Z/\ell and \ell-adic monodromy of every irreducible component of the moduli space M_g^f of curves of genus and and p-rank f. In particular, we prove that the Z/\ell-monodromy of every component of M_g^f is the symplectic group Sp_{2g}(Z/\ell) if g>=3 and \ell is a prime distinct from p. We give applications to the generic behavior of automorphism groups, Jacobians, class groups, and zeta functions of curves of given genus and p-rank.
The boundary of the $p$-rank $0$ stratum of the moduli space of cyclic covers of the projective line
Statistics of the zeros of zeta functions in families of hyperelliptic curves over a finite field
Moduli spaces for families of rational maps on P^1
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