Journal of the Ramanujan Mathematical Society
Volume 31, Issue 1, March 2016 pp. 79–94.
The growth of fine Selmer groups
Authors:
Meng Fai Lim and V. Kumar Murty
Author institution:School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, Hubei 430079, P.R.China
Summary:
Let A be an abelian variety defined over a number field F.
In this paper, we will investigate the growth of the p-rank of
the fine Selmer group in three situations. In particular, in each
of these situations, we show that there is a strong analogy
between the growth of the p-rank of the fine Selmer group and
the growth of the p-rank of the class groups.
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