$p$-divisible groups and relative crystalline representations
Liu, Tong ; Moon, Yong Suk
arXiv, Tome 2019 (2019) no. 0, / Harvested from
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 $R$.
Publié le : 2019-02-18
Classification:  Mathematics - Number Theory 
@article{1902.06546,
     author = {Liu, Tong and Moon, Yong Suk},
     title = {$p$-divisible groups and relative crystalline representations},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1902.06546}
}

Liu, Tong; Moon, Yong Suk. $p$-divisible groups and relative crystalline representations. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1902.06546/