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arXiv · 0707.2110

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

Jeff Achter·Rachel Pries
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Abstract

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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Jeff Achter, Rachel Pries. 2008-05-28. Monodromy of the p-rank strata of the moduli space of curves. https://doi.org/10.1093/imrn%2Frnn053

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