Yoshitaka Hachimori, Otmar Venjakob:
Completely faithful Selmer groups over Kummer extensions

       Autors: Yoshitaka Hachimori, Otmar Venjakob
       Titel:  Completely faithful Selmer groups over Kummer extensions
       Jahr: 2002
       Seiten: 36
       In: Doc. Math. Extra Volume: Kazuya Kato’s Fiftieth Birthday (2003), 443–478

        dvi-file   sel-hyper.dvi

        pdf-file   sel-hyper.pdf

      Abstract: In this paper 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 couples of the p-adic numbers. 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.