Non-existence and splitting theorems for normal integral bases
Number Theory
2009-02-26 v2
Abstract
We establish new conditions that prevent the existence of (weak) normal integral bases in tame Galois extensions of number fields. This leads to the following result: under appropriate technical hypotheses, the existence of a normal integral basis in the upper layer of an abelian tower Q \subset K \subset L forces the tower to be split in a very strong sense.
Keywords
Cite
@article{arxiv.0801.2272,
title = {Non-existence and splitting theorems for normal integral bases},
author = {Cornelius Greither and Henri Johnston},
journal= {arXiv preprint arXiv:0801.2272},
year = {2009}
}
Comments
17 pages, 4 figures, uses xypic, minor revisions following referee's report. To appear in Annales de L'Institut Fourier