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arXiv · 1902.06546

Relative crystalline representations and $p$-divisible groups in the small ramification case

Tong Liu·Yong Suk Moon
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Abstract

Let $k$ be a perfect field of characteristic $p > 2$, and let $K$ be a finite totally ramified extension over $W(k)[\frac{1}{p}]$ of ramification degree $e$. Let $R_0$ be a relative base ring over $W(k)\langle t_1^{\pm 1}, \ldots, t_m^{\pm 1}\rangle$ satisfying some mild conditions, and let $R = R_0\otimes_{W(k)}\mathcal{O}_K$. We show that if $e < p-1$, then every crystalline representation of $\pi_1^{\text{\'et}}(\mathrm{Spec}R[\frac{1}{p}])$ with Hodge-Tate weights in $[0, 1]$ arises from a $p$-divisible group over $R$.

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Tong Liu, Yong Suk Moon. 2019-02-18. Relative crystalline representations and $p$-divisible groups in the small ramification case. https://doi.org/10.2140/ant.2020.14.2773

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