On Shimura subvarieties generated by families of abelian covers of P1

We investigate the occurrence of Shimura (special) subvarieties in the locus of Jacobians of abelian Galois covers of ${\mathbb{P}}^1$ in $A_g$ and give classifications of families of such covers that give rise to Shimura subvarieties in the Torelli locus $T_g$ inside $A_g$. Our methods are based on Moonen–Oort works as well as characteristic p techniques of Dwork and Ogus and Monodromy computations.