Rationality problem for norm one tori in small dimensions

Hasegawa, Sumito; Hoshi, Akinari; Yamasaki, Aiichi

doi:10.1090/mcom/3469

Rationality problem for norm one tori in small dimensions
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Math. Comp. 89 (2020), 923-940 Request permission

Abstract:

We classify stably/retract rational norm one tori in dimension $n-1$ for $n=2^e$ $(e\geq 1)$ as a power of $2$ and $n=12, 14, 15$. Retract non-rationality of norm one tori for primitive $G\leq S_{2p}$ where $p$ is a prime number and for the five Mathieu groups $M_n\leq S_n$ $(n=11,12,22,23,24)$ is also given.

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