F-isocrystals of Higher Direct Images of $p$-Divisible Groups

Zhenghui Li; Yanshuai Qin

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arXiv · 2506.11736

F-isocrystals of Higher Direct Images of $p$-Divisible Groups

Zhenghui Li·Yanshuai Qin

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Abstract

For a $p$-divisible group $G$ over a smooth projective variety $X$ over $k$, where $k$ is a field finitely generated over a perfect field of characteristic $p$, we show that the formal group $R^i f_{\fppf*} G$ is isogenous to a $p$-divisible group. The Dieudonn\'e crystal of its divisible part is canonically isomorphic to the slope-$[0,1]$ part of $R^i f_{\crys*} \cM^{cr}(G)$ in the category of $F$-isocrystals over $k$. This provides an answer to the rational form of a question of Artin--Mazur regarding the enlarged formal Brauer groups.

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BibTeX RIS

Zhenghui Li, Yanshuai Qin. 2025-06-13. F-isocrystals of Higher Direct Images of $p$-Divisible Groups. https://arxiv.org/abs/2506.11736

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