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This is a Quantitative Study study.

September 16, 2025Open Access

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

Key Points

The introduction of universal G-zips on good reductions of PEL-type shimura varieties enhances understanding of their mod p geometry.
An extended study of Ekedahl-Oort stratification reveals important aspects of the geometry associated with splitting models.
By combining new constructions with previous research on Hasse invariants, significant findings related to Galois representations are attained.
The research ultimately contributes to the development of compactifications in the context of arithmetic geometry.

Abstract

Abstract 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 compactifications 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.

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Shen et al. (Wed,) studied this question.

synapsesocial.com/papers/68d4565b31b076d99fa5b246 https://doi.org/https://doi.org/10.1017/fms.2025.10091

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