On Lie algebras arising from p-adic representations in the imperfect residue field case

JOURNAL OF ALGEBRA

卷:406

Article

Ohkubo, Shun

关键词: Algebraic number theory;    p-adic representation;    Sen's theory;   

DOI  :  10.1016/j.jalgebra.2014.02.021

来源: Elsevier

【 摘 要 】

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) < infinity. Let G(K) be the absolute Galois group of K and p : G(K) -> GL(h)(Q(p)) a p-adic representation. When k(K) is perfect, Shankar Sen described the Lie algebra of rho(G(K)) in terms of so-called Sen's operator circle minus for rho. When kK may not be perfect, Olivier Brinon defined d + 1 operators circle minus(0),...,circle minus(d) for rho, which reduce to Sen's operator e in the case of d = 0. In this paper, we describe the Lie algebra of rho(G(K)) in terms of Brinon's operators circle minus(0),...,circle minus(d), which is a generalization of Sen's result. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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