We study the intersection of the Torelli locus with the Newton polygon stratification of the modulo $p$ reduction of certain PEL-type Shimura varieties. Using a clutching method, we produce infinitely many new examples of Newton polygons that occur for smooth curves that are cyclic covers of the projective line. Most of these examples demonstrate unlikely intersections of the open Torelli locus with the Newton polygon stratification in Siegel modular varieties.
Newton polygon stratification of the Torelli locus in PEL-type Shimura varieties
Wanlin Li, Centre de Recherches MathématiquesAuthors: Wanlin Li, Elena Mantovan, Rachel Pries, Yunqing Tang
2022 AWM Research Symposium
New Directions in Number Theory