On Galois structure of the integers in elementary Abelian extensions of local number fields

JOURNAL OF NUMBER THEORY

卷:125

Article

Miyata, Yoshimasa

关键词: local fields;    free module;    isomorphism classy;    invariant factor;   

DOI  :  10.1016/j.jnt.2006.12.005

来源: Elsevier

【 摘 要 】

Let p be an odd prime number and k a finite extension of Q(p). Let K/k be a totally ramified elementary abelian Kummer extension of degree p(2) with Galois group G. We determine the isomorphism class of the ring of integers in K as an oG-module under some assumptions. The obtained results imply there exist extensions whose rings are Z(p)G-isomorphic but not oG-isomorphic, where Z(p) is the ring of p-adic integers. Moreover we obtain conditions that the rings of integers are free over the associated orders and give extensions whose rings are not free. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free