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arXiv · 1410.4829

On the relative Galois module structure of rings of integers in tame extensions

A. Agboola·L. R. McCulloh
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Abstract

Let $F$ be a number field with ring of integers $O_F$ and let $G$ be a finite group. We describe an approach to the study of the set of realisable classes in the locally free class group $Cl(O_FG)$ of $O_FG$ that involves applying the work of the second-named author in the context of relative algebraic $K$ theory. When $G$ is of odd order, we show (subject to certain conditions) that the set of realisable classes is a subgroup of $Cl(O_FG)$. This may be viewed as being a partial analogue of a classical theorem of Shafarevich on the inverse Galois problem for soluble groups in the setting of Galois module theory.

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A. Agboola, L. R. McCulloh. 2018-07-11. On the relative Galois module structure of rings of integers in tame extensions. https://doi.org/10.2140/ant.2018.12.1823

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