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This article is cited in 5 scientific papers (total in 5 papers)
On tori with a biquadratic splitting field
B. È. Kunyavskii
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 $(n\geqslant0)$ 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.
Received: 09.03.1977
Citation:
B. È. Kunyavskii, “On tori with a biquadratic splitting field”, Izv. Akad. Nauk SSSR Ser. Mat., 42:3 (1978), 580–587; Math. USSR-Izv., 12:3 (1978), 536–542
Linking options:
https://www.mathnet.ru/eng/im1780https://doi.org/10.1070/IM1978v012n03ABEH001999 https://www.mathnet.ru/eng/im/v42/i3/p580
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Abstract page: | 291 | Russian version PDF: | 104 | English version PDF: | 12 | References: | 42 | First page: | 1 |
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