Geodesic
Behavior of the curve $x^3+y^3=1$ in a~cyclotomic $\Gamma$-extension
Sbornik. Mathematics, Tome 19 (1973) no. 1, pp. 117-130

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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. 
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     author = {M. I. Bashmakov and N. Zh. Al'-Nader},
     title = {Behavior of the curve $x^3+y^3=1$ in a~cyclotomic $\Gamma$-extension},
     journal = {Sbornik. Mathematics},
     pages = {117--130},
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     volume = {19},
     number = {1},
     year = {1973},
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     url = {http://geodesic.mathdoc.fr/item/SM_1973_19_1_a7/}
}
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M. I. Bashmakov; N. Zh. Al'-Nader. Behavior of the curve $x^3+y^3=1$ in a~cyclotomic $\Gamma$-extension. Sbornik. Mathematics, Tome 19 (1973) no. 1, pp. 117-130. http://geodesic.mathdoc.fr/item/SM_1973_19_1_a7/