Crystalline and semi-stable representations in the imperfect residue field case
Crystalline and semi-stable representations in the imperfect residue field case
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不完美残留场情况下的晶体和半稳定表示
DOI：
10.4310/ajm.2014.v18.n1.a8
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
K. Morita
中科院分区：
文献类型：
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作者：
K. Morita
设K是具有剩余域k的p-adic局部域，使得[k：k^p]=p^e<\infty，V是Gal（\bar{K}/K）的p-adic表示。然后，利用p-adic微分模的理论，证明了V是一个潜在的结晶（分别为：Gal（\bar{K}/K）的潜在半稳定）表示当且仅当V是潜在晶体（分别潜在半稳定）表示Gal（\bar{K^{pf}}/K^{pf}），其中K^{pf}/K是某个p-adic局部域，其剩余域是包含k的最小完美域k^{pf}。作为应用，我们证明了方丹的p-adic单值定理在不完全剩余域情形下的结果.
Let K be a p-adic local field with residue field k such that [k:k^p]=p^e<\infty and V be a p-adic representation of Gal(\bar{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 Gal(\bar{K}/K) if and only if V is a potentially crystalline (resp. potentially semi-stable) representation of Gal(\bar{K^{pf}}/K^{pf}) where K^{pf}/K is a certain p-adic local field whose residue field is the smallest perfect field k^{pf} containing k. As an application, we prove the p-adic monodromy theorem of Fontaine in the imperfect residue field case.