The intersection of the Torelli locus with the non-ordinary locus in PEL-type Shimura varieties

NUMBER THEORY

Speaker:

Rachel Pries - Colorado State University

Every Newton polygon satisfying the Kottwitz conditions occurs on Shimura varieties of PEL-type in positive characteristic (Viehmann/Wedhorn). In most cases, it is not known whether these Newton polygon strata contain points representing the Jacobians of smooth curves. In some cases, this is not even known for the mu-ordinary stratum. We provide a positive answer for the mu-ordinary and almost mu-ordinary strata in infinitely many cases. For base cases, we consider the arithmetic of some of Moonen's families of cyclic covers of the projective line. 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.