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arXiv · 2302.06231

Rationality problem for norm one tori for dihedral extensions

Akinari Hoshi·Aiichi Yamasaki
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Abstract

We give a complete answer to the rationality problem (up to stable $k$-equivalence) for norm one tori $R^{(1)}_{K/k}(\mathbb{G}_m)$ of $K/k$ whose Galois closures $L/k$ are dihedral extensions with the aid of Endo and Miyata [EM75, Theorem 1.5, Theorem 2.3] and Endo [End11, Theorem 2.1]. By using a similar technique, we give refinements of the proof of stably rational cases of Endo and Miyata's theorems as an appendix of the paper.

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Akinari Hoshi, Aiichi Yamasaki. 2023-02-13. Rationality problem for norm one tori for dihedral extensions. https://arxiv.org/abs/2302.06231

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