Geodesic
On the rank of elliptic curves over $\Gamma$-extensions
Sbornik. Mathematics, Tome 22 (1974) no. 3, pp. 465-472 
P. F. Kurchanov. On the rank of elliptic curves over $\Gamma$-extensions. Sbornik. Mathematics, Tome 22 (1974) no. 3, pp. 465-472. http://geodesic.mathdoc.fr/item/SM_1974_22_3_a7/
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     author = {P. F. Kurchanov},
     title = {On the rank of elliptic curves over $\Gamma$-extensions},
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     year = {1974},
     volume = {22},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1974_22_3_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper an estimate is given for the $\rho$-invariant of the Mazur module for Abelian varieties over $\Gamma$-extensions. For an elliptic Fermat curve the group of points at each level of a noncyclotomic $\Gamma$-extension is computed. Bibliography: 6 titles.

[1] M. I. Bashmakov, N. Zh. Al-Nader, “Povedenie krivoi $x^3+y^3=1$ v krugovom $\Gamma$-rasshirenii”, Matem. sb., 90 (132) (1973), 117–130 | MR | Zbl

[2] V. G. Berkovich, “O delenii na izogeniyu tochek ellipticheskoi krivoi”, Matem. sb., 93 (135) (1974), 467–486 | Zbl

[3] P. F. Kurchanov, “Ellipticheskie krivye beskonechnogo ranga nad $\Gamma$-rasshireniyami”, Matem. sb., 90 (132) (1973), 320–324 | Zbl

[4] Yu. I. Manin, “Krugovye polya i modelyarnye krivye”, Uspekhi matem. nauk, XXVI:6 (162) (1971), 7–71 | MR

[5] B. Mazur, “Rational Points of Abelian Varieties with Values in Towers of Number Fields”, Inven. math., 18 (1972), 183–266 | DOI | MR | Zbl

[6] O. Neuman, “Eine Bemerkung über die Galois-Kohomologie von endlichen Moduln”, Math. Nachr., 47:1–6 (1970), 279–282 | DOI | MR | Zbl