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Mathematics of the USSR-Izvestiya, 1978, Volume 12, Issue 3, Pages 536–542
DOI: https://doi.org/10.1070/IM1978v012n03ABEH001999
(Mi im1780)
 

This article is cited in 5 scientific papers (total in 5 papers)

On tori with a biquadratic splitting field

B. È. Kunyavskii
References:
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
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1978, Volume 42, Issue 3, Pages 580–587
Bibliographic databases:
UDC: 513.6
MSC: 20G15, 14M20, 14L10
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
\Bibitem{Kun78}
\by B.~\`E.~Kunyavskii
\paper On tori with a~biquadratic splitting field
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 3
\pages 580--587
\mathnet{http://mi.mathnet.ru/im1780}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=498387}
\zmath{https://zbmath.org/?q=an:0419.14007|0387.14001}
\transl
\jour Math. USSR-Izv.
\yr 1978
\vol 12
\issue 3
\pages 536--542
\crossref{https://doi.org/10.1070/IM1978v012n03ABEH001999}
Linking options:
  • https://www.mathnet.ru/eng/im1780
  • https://doi.org/10.1070/IM1978v012n03ABEH001999
  • https://www.mathnet.ru/eng/im/v42/i3/p580
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:291
    Russian version PDF:104
    English version PDF:12
    References:42
    First page:1
     
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