On the completely faithfulness of the p-free quotient modules of dual Selmer groups

Meng Fai Lim

Published 2015-04-20Version 1

In this paper, we consider the question of completely faithfulness of the p-free quotient module of the dual Selmer groups of elliptic curves defined over a noncommutative p-adic Lie extension. Our question will refine the previous question on the completely faithfulness of dual Selmer groups. We will also formulate and study an analogous question for the dual Selmer groups of Hida deformations. We will give positive answer to our question in certain cases. We will also establish a control theorem between the two questions in certain cases.