The growth of fine Selmer groups

Published 10 Apr 2015 in math.NT | (1504.02522v2)

Abstract: Let A be an abelian variety defined over anumber field F. In this paper, we will investigate the growth of 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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