Journal of the Ramanujan Mathematical Society

Volume 40, Issue 2, June 2025 pp. 151–167.

Fine Selmer groups of Hida families and Coleman families

Authors: Abhishek
Author institution:Department of Mathematics and Statistics, IIT Kanpur, Kanpur 208 016, India.

Summary: In this article, we study the fine Selmer groups associated with the ‘big’ Galois representation attached to a Hida family and a Coleman family. Inspired by some classical conjectures in Iwasawa theory, Coates-Sujatha made predictions regarding the structure of fine Selmer groups of elliptic curves over p-adic Lie-extension of number fields. We discuss suitable analogues of these conjectures for the ‘big’ Galois representation associated to a Hida family and a Coleman family.

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