2023/04/02 by Ghosh, Sohan
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2304.00499
The p^∞-fine Selmer group of an elliptic curve E over a global field is a subgroup of the classical p^∞-Selmer group. Coates and Sujatha discovered that the structure of the fine Selmer group of E over certain p-adic Lie extensions of a number field is intricately related to some deep questions in classical Iwasawa theory. Inspired by a conjecture of Greenberg, they made prediction about the structure of the fine Selmer group over certain p-adic Lie extensions of a number field, which they called Conjecture B. In this article, we discuss some new cases of Conjecture B and its analogues over some p-adic Lie extensions of function fields of characteristic p.