Abstract
Voskresenskii conjectured that stably rational tori are rational. Klyachko proved this assertion for a wide class of tori by general principles. We re-prove Klyachko’s result by providing simple explicit birational isomorphisms, and elaborate on some links to torus-based cryptography.
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The first author is partially supported by the French National Agency (Project GeoLie ANR-15-CE40-0012).
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Florence, M., van Garrel, M. A constructive approach to a conjecture by Voskresenskii. Sel. Math. New Ser. 23, 2899–2906 (2017). https://doi.org/10.1007/s00029-017-0330-x
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DOI: https://doi.org/10.1007/s00029-017-0330-x
Keywords
- Linear algebraic groups
- Stable rationality
- Rationality
- Algebraic tori
- Voskresenskii conjecture
- Torus-based cryptography