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Journal of the Ramanujan Mathematical Society

Volume 36, Issue 1, March 2021  pp. 39–47.

Growth of p-fine Selmer groups and p-fine Shafarevich-Tate groups in Z/pZ-extensions

Authors:  Debanjana Kundu
Author institution:Department of Mathematics, University of British Columbia, Vancouver BC, V6T 1Z2, Canada

Summary:  In this paper we show that the p-fine Selmer Group can become arbitrarily large as we vary over all Z/pZ extensions of a given number field K and find effective estimates on the conductor of such a Z/pZ-extension. In fact, we show that the p-fine Shafarevich-Tate group can become arbitrarily large on varying over all Z/pZ extensions of a given number field. We explore the close relationship in the size of p-fine Selmer groups and p-torsion of ideal class groups in quadratic extensions of number fields.


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