Indices of inseparability and refined ramification breaks

JOURNAL OF NUMBER THEORY

卷:142

Article

Keating, Kevin

关键词: Local fields;    Ramification;    Index of inseparability;    Kummer theory;    Refined ramification breaks;    Truncated exponentiation;    Class field theory;    Galois modules;   

DOI  :  10.1016/j.jnt.2014.02.007

来源: Elsevier

【 摘 要 】

Let K be a finite extension of Q(p) which contains a primitive pth root of unity zeta(p). Let L/K be a totally ramified (Z/pZ)(2)-extension which has a single ramification break b. In [2] Byott and Elder defined a refined ramification break b(*) for LIK. In this paper we prove that if p>2 and the index of inseparability i(1) of L/K is not equal to p(2)b - pb then b(*) = i(1) - p(2)b + pb + b. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free