Hachimori, Yoshitaka; Venjakob, Otmar

Completely faithful Selmer groups over Kummer extensions

Doc. Math. (Bielefeld) Extra Vol. Kazuya Kato's Fiftieth Birthday, 443-478 (2003)


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.

Mathematics Subject Classification

11G05, 14K15