The Hasse norm principle for $A_n$-extensions

Abstract

We prove that, for every $n\ge 5$, the Hasse norm principle holds for a degree $n$ extension $K/k$ of number fields with normal closure $F$ such that $\mathrm{Gal}(F/k)\cong A_n$. We also show the validity of weak approximation for the associated norm one tori.

14 pages, comments welcome