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

In this paper, we consider the question of complete 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 complete faithfulness of dual Selmer groups. We will also consider the question of the triviality of the central torsion submodules of these Iwasawa modules. We also formulate and study analogous questions for the dual Selmer groups of Hida deformations. We then give positive answer to our questions in certain cases. We will also establish "control theorem" results between the questions.