A note on the Hasse norm principle

Abstract

Let $A$ be a finite, abelian group. We show that the density of $A$-extensions satisfying the Hasse norm principle exists, when the extensions are ordered by discriminant. This strengthens earlier work of Frei--Loughran--Newton \cite{FLN}, who obtained a density result under the additional assumption that $A/A[\ell ]$ is cyclic with $\ell$ denoting the smallest prime divisor of $\#A$.

8 pages. Final version, to appear Bull. Lon. Math. Soc

References in corpus (1)

• On the probabilities of local behaviors in abelian field extensions