On tori with a biquadratic splitting field

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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⩾0) of a special three-dimensional torus I and an affine space Am. 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
Original languageAmerican English
Pages (from-to)580-587
JournalAkad. Nauk SSSR Ser. Mat
Issue number3
StatePublished - 1978


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