Relative crystalline representations and $p$-divisible groups in the small ramification case
| Autor: | Yong Suk Moon, Tong Liu |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
11F80
Mathematics::Number Theory 01 natural sciences Combinatorics Base (group theory) Mathematics::Algebraic Geometry 0103 physical sciences FOS: Mathematics relative $p$-adic Hodge theory Number Theory (math.NT) 0101 mathematics crystalline representation 14L05 Mathematics Ring (mathematics) Algebra and Number Theory Degree (graph theory) Mathematics - Number Theory Group (mathematics) 010102 general mathematics Extension (predicate logic) 11S20 $p$-divisible group Perfect field 010307 mathematical physics Ramification |
| Zdroj: | Algebra Number Theory 14, no. 10 (2020), 2773-2789 |
| ISSN: | 2773-2789 |
| 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 $��_1^{\text{��t}}(\mathrm{Spec}R[\frac{1}{p}])$ with Hodge-Tate weights in $[0, 1]$ arises from a $p$-divisible group over $R$. 19 pages; changed the title; added section 6 and more details |
| Databáze: | OpenAIRE |
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