Iwasawa theory for elliptic curves over imaginary quadratic fields
Journal de théorie des nombres de Bordeaux, Volume 13 (2001) no. 1, p. 1-25

Let E be an elliptic curve over , let K be an imaginary quadratic field, and let K be a p -extension of K. Given a set Σ of primes of K, containing the primes above p, and the primes of bad reduction for E, write K Σ for the maximal algebraic extension of K which is unramified outside Σ. This paper is devoted to the study of the structure of the cohomology groups H i (K Σ /K ,E p ) for i=1,2, and of the p-primary Selmer group Sel p (E/K ), viewed as discrete modules over the Iwasawa algebra of K /K.

Soit E une courbe elliptique sur , soit K un corps quadratique imaginaire, et soit K une p -extension de K. Étant donné un ensemble Σ de places de K contenant les places au dessus de p et les places de mauvaise réduction de E, nous notons K Σ l’extension maximale de K non ramifiée en-dehors de Σ. Cet article est consacré à l’étude de la structure des groupes de cohomologie H i (K Σ /K ,E p ) pour i=1,2, et de la composante p-primaire du groupe de Selmer Sel p (E/K ), considérés comme modules discrets sur l’algèbre d’Iwasawa de K /K.

@article{JTNB_2001__13_1_1_0,
     author = {Bertolini, Massimo},
     title = {Iwasawa theory for elliptic curves over imaginary quadratic fields},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {13},
     number = {1},
     year = {2001},
     pages = {1-25},
     zbl = {1061.11058},
     mrnumber = {1838067},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2001__13_1_1_0}
}
Bertolini, Massimo. Iwasawa theory for elliptic curves over imaginary quadratic fields. Journal de théorie des nombres de Bordeaux, Volume 13 (2001) no. 1, pp. 1-25. http://www.numdam.org/item/JTNB_2001__13_1_1_0/

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