Geodesic
On two-dimensional algebraic tori. II
Izvestiya. Mathematics , Tome 1 (1967) no. 3, pp. 691-696.

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It is proven that two-dimensional algebraic tori are rational over their field of definition. 
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V. E. Voskresenskii. On two-dimensional algebraic tori. II. Izvestiya. Mathematics , Tome 1 (1967) no. 3, pp. 691-696. http://geodesic.mathdoc.fr/item/IM2_1967_1_3_a10/

[1] Voskresenskii V. E., “O dvumernykh algebraicheskikh torakh”, Izv. AN SSSR. Ser. matem., 29 (1965), 239–244 | MR

[2] Chevalley C., “On algebraic group varieties”, J. Math. Spc. Japan, 6 (1954), 303–324 | MR | Zbl

[3] Algebraicheskie poverkhnosti, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 75, 1965 | MR | Zbl

[4] Nagata M., “Ratsionalnye poverkhnosti”, Matematika, 8:4 (1964), 75–94

[5] Baldassari M., Algebraicheskie mnogoobraziya, IL, M., 1961