On Lie algebras arising from p-adic representations in the imperfect residue field case
On Lie algebras arising from p-adic representations in the imperfect residue field case
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关于不完美留数场情况下由 p 进表示产生的李代数
DOI：
10.1016/j.jalgebra.2014.02.021
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发表时间：
2014
影响因子：
0.9
通讯作者：
Shun
中科院分区：
文献类型：
--
作者：
OHKUBO;Shun
设K为混合特征（0,p）具有残差域K K的完全离散估值域，使得[K K: K K p]= p d<∞。设gk为K和ρ的绝对伽罗瓦群：gk→GL h （Q p）一个p进表示。当k k是完美的，Shankar Sen用所谓的Sen算子Θ描述了ρ (G k)的李代数。当k k可能不完美时，Olivier Brinon为ρ定义了d+ 1个算子Θ 0，…，Θ d，在d= 0的情况下简化为Sen算子Θ。本文用Brinon算子Θ 0，…，Θ d描述了ρ (G K)的Lie代数，这是Sen的结果的推广。
Let K be a complete discrete valuation field of mixed characteristic (0, p) with residue field k K such that [k K: k K p]= p d<∞. Let G K be the absolute Galois group of K and ρ: G K→ GL h (Q p) a p-adic representation. When k K is perfect, Shankar Sen described the Lie algebra of ρ (G K) in terms of so-called Sen's operator Θ for ρ. When k K may not be perfect, Olivier Brinon defined d+ 1 operators Θ 0,…, Θ d for ρ, which reduce to Sen's operator Θ in the case of d= 0. In this paper, we describe the Lie algebra of ρ (G K) in terms of Brinon's operators Θ 0,…, Θ d, which is a generalization of Sen's result.