具有给定Galois群的极大非分歧p-扩张的构造
数论
2009-07-17 v2
摘要
在本文中，我们将证明对于任意素数p，每个有限p-群都可以作为某个有限次数数域的极大非分歧p-扩张的Galois群。我们还将证明，对于任意给定的具有可数多个生成元的pro-p群G，存在一个数域（未必是有限次数的），其极大非分歧p-扩张的Galois群同构于G。这意味着数域（包括无限次数的数域）上的极大非分歧p-扩张的Galois群同构类的集合，恰好等于所有具有可数多个生成元的pro-p群的同构类集合。
引用
@article{arxiv.0705.2293,
title = {Construction of maximal unramified p-extensions with prescribed Galois groups},
author = {Manabu Ozaki},
journal= {arXiv preprint arXiv:0705.2293},
year = {2009}
}
备注
In this new version, a considerable improvement has been done, that is, Theorems 1 and 2 have been established for all the prime number p (without restrictive assumption C(p) on the prime number p)