$F$-zips with additional structure on splitting models of Shimura varieties

Xu Shen, Yuqiang Zheng

Published 2022-12-28Version 1

We construct universal $G$-zips on good reductions of the Pappas-Rapoport splitting models for PEL-type Shimura varieties. We study the induced Ekedahl-Oort stratification, which sheds new light on the mod $p$ geometry of splitting models. Building on the work of Lan on arithmetic compatifications of splitting models, we further extend these constructions to smooth toroidal compactifications. Combined with the work of Goldring-Koskivirta on group theoretical Hasse invariants, we get an application to Galois representations associated to torsion classes in coherent cohomology in the ramified setting.