Crystalline and semi-stable representations in the imperfect residue field case
| Autor: | Kazuma Morita |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
11F80
Mathematics - Number Theory $p$-adic cohomology Applied Mathematics General Mathematics Mathematics::Number Theory $p$-adic Galois representation Monodromy theorem 14F30 Combinatorics Residue field FOS: Mathematics Perfect field 12H25 $p$-adic differential equation Number Theory (math.NT) Local field Mathematics |
| Zdroj: | Asian J. Math. 18, no. 1 (2014), 143-158 |
| DOI: | 10.48550/arxiv.1105.0846 |
| Popis: | Let $K$ be a $p$-adic local field with residue field $k$ such that $[k : k^p] = p^e \lt \infty$ and $V$ be a $p$-adic representation of $\mathrm{Gal}(\overline{K} / K)$. Then, by using the theory of $p$-adic differential modules, we show that $V$ is a potentially crystalline (resp. potentially semi-stable) representation of $\mathrm{Gal}(\overline{K} / K)$ if and only if $V$ is a potentially crystalline (resp. potentially semi-stable) representation of $\mathrm{Gal}(\overline{K^\mathrm{pf}} / K^\mathrm{pf})$ where $K^\mathrm{pf} / K$ is a certain $p$-adic local field whose residue field is the smallest perfect field $k^\mathrm{pf}$ containing $k$. As an application, we prove the $p$-adic monodromy theorem of Fontaine in the imperfect residue field case. |
| Databáze: | OpenAIRE |
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