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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