Special Subvarieties Arising from Families of Cyclic Covers of the Projective Line

We consider families of cyclic covers of $\Bbb P^1$, where we fix the covering group and the local monodromies and we vary the branch points. We prove that there are precisely twenty such families that give rise to a special subvariety in the moduli space of abelian varieties. Our proof uses techniques in mixed characteristics due to Dwork and Ogus.

2010 Mathematics Subject Classification: 11G15, 14H40, 14G35

Keywords and Phrases: Special subvarieties, Jacobians, complex multiplication

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