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Tame Galois module structure revisited
- Source :
- Ann. Mat. Pura Appl. (2019), https://doi.org/10.1007/s10231-019-00852-x
- Publication Year :
- 2018
-
Abstract
- A number field $K$ is Hilbert-Speiser if all of its tame abelian extensions $L/K$ admit NIB (normal integral basis). It is known that $\mathbb{Q}$ is the only such field, but when we restrict $\text{Gal}(L/K)$ to be a given group $G$, the classification of $G$-Hilbert-Speiser fields is far from complete. In this paper, we present new results on so-called $G$-Leopoldt fields. In their definition, NIB is replaced by ``weak NIB'' (defined below). Most of our results are negative, in the sense that they strongly limit the class of $G$-Leopoldt fields for some particular groups $G$, sometimes even leading to an exhaustive list of such fields or at least to a finiteness result. In particular we are able to correct a small oversight in a recent article by Ichimura concerning Hilbert-Speiser fields.<br />Comment: 16 pages. Same version as the published paper
- Subjects :
- Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- Ann. Mat. Pura Appl. (2019), https://doi.org/10.1007/s10231-019-00852-x
- Publication Type :
- Report
- Accession number :
- edsarx.1805.12588
- Document Type :
- Working Paper