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Rationality problem for norm one tori in small dimensions


Authors: Sumito Hasegawa, Akinari Hoshi and Aiichi Yamasaki
Journal: Math. Comp. 89 (2020), 923-940
MSC (2010): Primary 11E72, 12F20, 13A50, 14E08, 20C10, 20G15
DOI: https://doi.org/10.1090/mcom/3469
Published electronically: September 12, 2019
MathSciNet review: 4044456
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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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Additional Information

Sumito Hasegawa
Affiliation: Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan
Email: shasegawa@m.sc.niigata-u.ac.jp

Akinari Hoshi
Affiliation: Department of Mathematics, Niigata University, Niigata 950-2181, Japan
Email: hoshi@math.sc.niigata-u.ac.jp

Aiichi Yamasaki
Affiliation: Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
Email: aiichi.yamasaki@gmail.com

DOI: https://doi.org/10.1090/mcom/3469
Keywords: Rationality problem, algebraic tori, stably rational, retract rational, flabby resolution
Received by editor(s): January 1, 2019
Received by editor(s) in revised form: April 14, 2019, May 14, 2019, and May 26, 2019
Published electronically: September 12, 2019
Additional Notes: This work was partially supported by JSPS KAKENHI Grant Numbers 25400027, 16K05059, 19K03418.
Article copyright: © Copyright 2019 American Mathematical Society