Special Loci in the Moduli of Curves
David Urbanik, Ziquan Yang
Source abstract
We introduce new techniques to study mixed-characteristic special loci in moduli spaces and give several applications, focusing in particular on the moduli space of curves. These applications include Zariski density results for split Jacobians, non-density results for supersingular loci, and lifting results for algebraic cycles, all under appropriate numerical conditions. Our methods generalize to more-or-less arbitrary moduli spaces mapping to Hodge-type Shimura varieties (and even some settings beyond the Shimura case), and relate to questions raised by Oort and de Jong.
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