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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
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
Citation:
M. I. Bashmakov, N. Zh. Al'-Nader, “Behavior of the curve $x^3+y^3=1$ in a cyclotomic $\Gamma$-extension”, Math. USSR-Sb., 19:1 (1973), 117–130
Linking options:
https://www.mathnet.ru/eng/sm2999https://doi.org/10.1070/SM1973v019n01ABEH001739 https://www.mathnet.ru/eng/sm/v132/i1/p117
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