Enumeration of isomorphism classes of extensions of p-adic fields

JOURNAL OF NUMBER THEORY

卷:104

Article

Hou, XD ; Keating, K

关键词: class field theory;    enumeration;    isomorphism class;    local field;    p-adic field;   

DOI  :  10.1016/S0022-314X(03)00155-0

来源: Elsevier

【 摘 要 】

Let Omega be an algebraic closure of Q(p) and let F be a finite extension of Q(p) contained in Omega. Given positive integers f and e, the number of extensions K/F contained in Omega with residue degree f and ramification index e was computed by Krasner. This paper is concerned with the number F(F,f,e) of F-isomorphism classes of such extensions. We determine 3(F,f,e) completely when p(2) inverted iota e and get partial results when p(2) \\ e. When s is large, F(Q(p), f, e) is equal to the number of isomorphism classes of finite commutative chain rings with residue field F-pf, ramification index e, and lengths. (C) 2003 Elsevier Inc. All rights reserved.

【 授权许可】

Free