Indices of inseparability in towers of field extensions

JOURNAL OF NUMBER THEORY

卷:150

Article

Keating, Kevin

关键词: Local field;    Ramification theory;    Index of inseparability;    Hasse-Herbrand functions;   

DOI  :  10.1016/j.jnt.2014.11.009

来源: Elsevier

【 摘 要 】

Let K be a local field whose residue field has characteristic p and let L/K be a finite separable totally ramified extension of degree n = ap(v). The indices of inseparability i(0), i(1), ...., i(v) of L/K were defined by Fried in the case char(K) = p and by Heiermann in the case char(K) = 0; they give a refinement of the usual ramification data for L/K. The indices of inseparability can be used to construct generalized Hasse-Herbrand functions Phi(j)(L/K) for 0 <= j <= v. In this paper we give an interpretation of the values Phi(j)(L/K) (c) for nonnegative integers c. We use this interpretation to study the behavior of generalized Hasse-Herbrand functions in towers of field extensions. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free