Relative crystalline representations and $p$-divisible groups in the small ramification case
| Autor: | Liu, Tong, Moon, Yong Suk |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Alg. Number Th. 14 (2020) 2773-2789 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/ant.2020.14.2773 |
| Popis: | 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 $R$. Comment: 19 pages; changed the title; added section 6 and more details |
| Databáze: | arXiv |
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