On counting rings of integers as Galois modules

Abstract

Let $K$ be a number field and $G$ a finite abelian group. We study the asymptotic behaviour of the number of tamely ramified $G$-extensions of $K$ with ring of integers of fixed realisable class as a Galois module.

arXiv commentFinal version. Substantial revision, taking into account a number of helpful suggestions by an anonymous referee. To appear in Crelle