Monodromy of the p-rank strata of the moduli space of curves

Details Monodromy of the p-rank strata of the moduli space of curves Monodromy of the p-rank strata of the moduli space of curves

2007-07-13

arxiv.org/abs/0707.2110v2

Mathematics

Number Theory

Scientific paper

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.

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