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Mathematics of the USSR-Sbornik, 1973, Volume 19, Issue 1, Pages 117–130
DOI: https://doi.org/10.1070/SM1973v019n01ABEH001739 (Mi sm2999) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Behavior of the curve $x^3+y^3=1$ in a cyclotomic $\Gamma$-extension

M. I. Bashmakov, N. Zh. Al'-Nader
English version PDF (794 kB) Citations (9)
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DOI: https://doi.org/10.1070/SM1973v019n01ABEH001739
Abstract: This article proves that the group of rational points on the curve in the title remains finite when the $3^n$th roots of unity are adjoined. Here the 3-component of the Tate–Shafarevich group remains finite, and exact formulas are given for its order.
Bibliography: 2 titles.
Received: 29.05.1972
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1973, Volume 90(132), Number 1, Pages 117–130
Bibliographic databases:
UDC: 513.015.7
MSC: 14G05, 14H45, 12A35
Language: English
Original paper language: Russian
Citation: M. I. Bashmakov, N. Zh. Al'-Nader, “Behavior of the curve $x^3+y^3=1$ in a cyclotomic $\Gamma$-extension”, Mat. Sb. (N.S.), 90(132):1 (1973), 117–130; Math. USSR-Sb., 19:1 (1973), 117–130
Citation in format AMSBIB
\Bibitem{BasAl-73}
\by M.~I.~Bashmakov, N.~Zh.~Al'-Nader
\paper Behavior of the curve $x^3+y^3=1$ in a~cyclotomic $\Gamma$-extension
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 90(132)
\issue 1
\pages 117--130
\mathnet{http://mi.mathnet.ru/sm2999}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=332799}
\zmath{https://zbmath.org/?q=an:0268.14010}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 19
\issue 1
\pages 117--130
\crossref{https://doi.org/10.1070/SM1973v019n01ABEH001739}
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  • https://www.mathnet.ru/eng/sm/v132/i1/p117
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:345
    Russian version PDF:77
    English version PDF:4
    References:35
     
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