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 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 language | American English |
|---|---|
| Pages (from-to) | 580-587 |
| Journal | Akad. Nauk SSSR Ser. Mat |
| Volume | 42 |
| Issue number | 3 |
| State | Published - 1978 |