Geodesic
Completely faithful Selmer groups over Kummer extensions
Documenta mathematica, Kazuya Kato's Fiftieth Birthday (2003), pp. 443-478.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We study the Selmer groups of elliptic curves over Galois extensions of number fields whose Galois group $G$ is isomorphic to the semidirect product of two copies of the $p$-adic numbers $\bbfZ_p$. In particular, we give examples where its Pontryagin dual is a faithful torsion module under the Iwasawa algebra of $G$. Then we calculate its Euler characteristic and give a criterion for the Selmer group being trivial. Furthermore, we describe a new asymptotic bound of the rank of the Mordell-Weil group in these towers of number fields.
Classification : 11G05, 14K15 
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     author = {Hachimori, Yoshitaka and Venjakob, Otmar},
     title = {Completely faithful {Selmer} groups over {Kummer} extensions},
     journal = {Documenta mathematica},
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     volume = {Kazuya Kato's Fiftieth Birthday},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2003__S6__a12/}
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Hachimori, Yoshitaka; Venjakob, Otmar. Completely faithful Selmer groups over Kummer extensions. Documenta mathematica, Kazuya Kato's Fiftieth Birthday (2003), pp. 443-478. http://geodesic.mathdoc.fr/item/DOCMA_2003__S6__a12/