Journal of the Ramanujan Mathematical Society

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The Growth of Fine Selmer groups


Affiliations
1 School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, Hubei 430079, China
2 Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Canada
     

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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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  • The Growth of Fine Selmer groups

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Authors

Meng Fai Lim
School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, Hubei 430079, China
V. Kumar Murty
Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Canada

Abstract


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.