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Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 5, Pages 1037–1046 (Mi izv2146)  

This article is cited in 8 scientific papers (total in 8 papers)

Rationality of certain algebraic tori

V. E. Voskresenskii


Abstract: It is shown that the necessary condition for pure transcendence of a field of invariants given by Swan is also sufficient. We prove the rationality of factors of the type $T/G_m$, where $T$ the are tori of a certain special form, as well as the extension of the statement $H^1(k,\operatorname{Pic}\overline V)=0$ to all connected linear groups with cyclic algebraic splitting field.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:5, 1049–1056

Bibliographic databases:

UDC: 513.6
MSC: Primary 12F20; Secondary 14C20, 20G99
Received: 03.02.1971

Citation: V. E. Voskresenskii, “Rationality of certain algebraic tori”, Izv. Akad. Nauk SSSR Ser. Mat., 35:5 (1971), 1037–1046; Math. USSR-Izv., 5:5 (1971), 1049–1056

Citation in format AMSBIB
\Bibitem{Vos71}
\by V.~E.~Voskresenskii
\paper Rationality of certain algebraic tori
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1971
\vol 35
\issue 5
\pages 1037--1046
\mathnet{http://mi.mathnet.ru/izv2146}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=286798}
\zmath{https://zbmath.org/?q=an:0219.14012}
\transl
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 5
\pages 1049--1056
\crossref{https://doi.org/10.1070/IM1971v005n05ABEH001200}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. M. Galkin, “Ob odnom ideale v gruppovom koltse tsiklicheskoi gruppy”, UMN, 28:2(170) (1973), 233–234  mathnet  mathscinet  zmath
    2. V. E. Voskresenskii, “Fields of invariants for Abelian groups”, Russian Math. Surveys, 28:4 (1973), 79–105  mathnet  crossref  mathscinet  zmath
    3. Yu. I. Manin, M. A. Tsfasman, “Rational varieties: algebra, geometry and arithmetic”, Russian Math. Surveys, 41:2 (1986), 51–116  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Christine Bessenrodt, Lieven Bruyn, “Stable rationality of certain PGLn-quotients”, Invent math, 104:1 (1991), 179  crossref  mathscinet  zmath  isi
    5. Kenneth A. Brown, Martin Lorenz, “Grothendieck groups of invariant rings: Examples”, Communications in Algebra, 22:1 (1994), 279  crossref
    6. Esther Beneish, “On the Dual of the Procesi–Formanek Lattice”, Algebr Represent Theor, 2010  crossref
    7. Esther Beneish, “Noether Settings of Some Groups with an Unexpected Property”, Communications in Algebra, 39:12 (2011), 4552  crossref
    8. Beneish E., Ramsey N., “Lattices over cyclic groups and Noether settings”, J. Algebra, 452 (2016), 212–226  crossref  mathscinet  zmath  isi  scopus
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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