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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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