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arXiv · 1806.11563

The Hasse norm principle for $A_n$-extensions

André Macedo
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Abstract

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

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André Macedo. 2018-06-29. The Hasse norm principle for $A_n$-extensions. https://doi.org/10.1016/j.jnt.2019.10.020

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