The intersection of the Torelli locus with the non-ordinary locus in PEL-type Shimura varieties
Around 1980, mathematicians developed several techniques to study the Newton polygon stratification of the moduli space of principally polarized abelian varieties in positive characteristic p. In 2004, Faber and Van der Geer used these techniques to prove that the Torelli locus of Jacobians of smooth curves intersects every p-rank stratum. In 2013, Viehmann and Wedhorn proved that every Newton polygon satisfying the Kottwitz conditions occurs on Shimura varieties of PEL-type. In most cases, it is still not known whether the Torelli locus intersects these Newton polygon strata. We provide a positive answer for the mu-ordinary and non-mu ordinary strata in infinitely many cases. As an application, we produce infinitely many new examples of unusual Newton polygons which occur for Jacobians of smooth curves. This is joint work with Li, Mantovan, and Tang.