Geodesic
On tori with a~biquadratic splitting field
Izvestiya. Mathematics , Tome 12 (1978) no. 3, pp. 536-542

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A complete birational classification of algebraic tori with a biquadratic splitting field is obtained in this paper. It is shown that any torus of the indicated type is birationally equivalent to a direct product of $n$ copies $(n\geqslant0)$ of a special three-dimensional torus $\mathscr I$ and an affine space $\mathbf A^m$. An affirmative answer to one of Zarisskii's conjectures is also obtained for tori of this type. Up till now a birational classification of tori has been known only in the case of a metacyclic splitting field (i.e. in the case where all Sylow subgroups of the Galois group of the splitting field are cyclic). Bibliography: 12 titles. 
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     title = {On tori with a~biquadratic splitting field},
     journal = {Izvestiya. Mathematics },
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     language = {en},
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B. È. Kunyavskii. On tori with a~biquadratic splitting field. Izvestiya. Mathematics , Tome 12 (1978) no. 3, pp. 536-542. http://geodesic.mathdoc.fr/item/IM2_1978_12_3_a5/