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arXiv · 2505.04492

Compatibility of $F$-isocrystals on adjoint Shimura varieties

Jake Huryn·Kiran S. Kedlaya·Christian Klevdal·Stefan Patrikis
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Abstract

In this article, we extend past results of the last two authors to include compatibility of canonical $\ell$-adic local systems and canonical $F$-isocrystals on adjoint Shimura varieties in the superrigid regime. Our method relies on the crystallinity of canonical $p$-adic local systems due to Esnault--Groechenig as well as Margulis superrigidity and the crystalline-to-\'etale companion construction of Drinfeld, Abe--Esnault, and Kedlaya.

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Jake Huryn, Kiran S. Kedlaya, Christian Klevdal, Stefan Patrikis. 2025-04-25. Compatibility of $F$-isocrystals on adjoint Shimura varieties. https://arxiv.org/abs/2505.04492

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