On tori with a biquadratic splitting field

Research output: Contribution to journalArticlepeer-review

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 languageAmerican English
Pages (from-to)580-587
JournalAkad. Nauk SSSR Ser. Mat
Volume42
Issue number3
StatePublished - 1978

Fingerprint

Dive into the research topics of 'On tori with a biquadratic splitting field'. Together they form a unique fingerprint.

Cite this