Abstract
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 T and an affine space Am. An affirmative answer to one of Zariski'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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