F-isocrystals of Higher Direct Images of $p$-Divisible Groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916793373687808 |
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| author | Li, Zhenghui Qin, Yanshuai |
| author_facet | Li, Zhenghui Qin, Yanshuai |
| contents | 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 Dieudonné 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_11736 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | F-isocrystals of Higher Direct Images of $p$-Divisible Groups Li, Zhenghui Qin, Yanshuai Algebraic Geometry 14F30, 14F22 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 Dieudonné 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. |
| title | F-isocrystals of Higher Direct Images of $p$-Divisible Groups |
| topic | Algebraic Geometry 14F30, 14F22 |
| url | https://arxiv.org/abs/2506.11736 |