Geodesic
Stable equivalence of~algebraic tori
Izvestiya. Mathematics , Tome 8 (1974) no. 1, pp. 1-7

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We show that the Picard modules $\operatorname{Pic}V_L(T)$ of projective models of algebraic tori $T$, computed over a field of characteristic zero, also determine birational invariants over a field of positive characteristic. We study the semigroup of classes of stably equivalent tori, and in particular prove that, for tori that are split over a cyclic extension, this is a group. 
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V. E. Voskresenskii. Stable equivalence of~algebraic tori. Izvestiya. Mathematics , Tome 8 (1974) no. 1, pp. 1-7. http://geodesic.mathdoc.fr/item/IM2_1974_8_1_a0/