Journal of the Ramanujan Mathematical Society
Volume 32, Issue 3, September 2017 pp. 299–326.
On the complete faithfulness of the p-free quotient
modules of dual Selmer groups
Authors:
Meng Fai Lim
Author institution:School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical
Sciences, Central China Normal University, Wuhan, 430079, P. R. China
Summary:
In this paper, we consider the question of the 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 previous questions on the complete faithfulness of
dual Selmer groups. We also consider the question of the triviality of
the central torsion submodules of these Iwasawa modules and we see
that this latter question is intimately related to the former. We will also
formulate and study analogous questions for the dual Selmer groups of
Hida deformations. We then give positive answer to our questions, and
establish “control theorem” results between the questions.
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