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

By Debanjana Kundu. 2021

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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 Z p -extension of a totally real number field and obtain a formula for the Z p co-rank of the fine Selmer group of an elliptic curve.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6d5738730214bf99deba127570aad3f174347571