Stably rational algebraic tori
Journal de théorie des nombres de Bordeaux, Volume 11 (1999) no. 1, pp. 263-268

The rationality of a stably rational torus with a cyclic splitting field is proved.

On montre qu'un tore stablement rationnel avec un corps de décomposition cyclique est rationnel.

Valentin E. Voskresenskii. Stably rational algebraic tori. Journal de théorie des nombres de Bordeaux, Volume 11 (1999) no. 1, pp. 263-268. doi: 10.5802/jtnb.250
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[1] A. Beauville, J.-L. Colliot-Thélène, J.-J. Sansuc, Sir P. Swinnerton-Dyer, Variétés stablement rationnelles non rationnelles. Ann. Math. 121 (1985), 283-318. | MR | Zbl

[2] V. Voskresenski, The geometry of linear algebraic groups. Proc. Steklov Inst. Math. 132 (1973), 173-183. | MR | Zbl

[3] V. Voskresenski, Fields of Invariants of Abelian Groups. Russian Math. Surveys 28 (1973), 79-105. | MR | Zbl

[4] A. Klyachko, On the rationality of tori with a cyclic splitting field. Arithmetic and Geometry of Varieties, Kuibyshev Univ., 1988, 73-78 (Russian). | Zbl

[5] A. Chistov, On the birational equivalence of tori with a cyclic splitting field. Zapiski Nauchnykh Seminarov LOMI 64 (1976), 153-158 (Russian). | MR | Zbl

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