An analogue of Kida's formula for fine Selmer groups of elliptic curves

Abstract

In this paper, we prove an analogue of Kida's formula for the fine Selmer groups of elliptic curves. We study the growth behaviour of the fine Selmer groups in p-power degree extensions of the cyclotomic Zp-extension of a totally real number field and obtain a formula for the Zp co-rank of the fine Selmer group of an elliptic curve.