#### Number Theory Seminar

##### Venue: Microsoft Teams (Online)

The ($p^{\infty}$) fine Selmer group (also called the $0$-Selmer group) of an elliptic curve is a subgroup of the usual $p^{\infty}$ Selmer group of an elliptic curve and is related to the first and the second Iwasawa cohomology groups. Coates-Sujatha observed that the structure of the fine Selmer group over the cyclotomic $\mathbb{Z}_p$-extension of a number field $K$ is intricately related to Iwasawa’s $\mu$-invariant vanishing conjecture on the growth of $p$-part of the ideal class group of $K$ in the cyclotomic tower. In this talk, we will discuss the structure and properties of the fine Selmer group over certain $p$-adic Lie extensions of global fields. This talk is based on joint work with Sohan Ghosh and Sudhanshu Shekhar.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 03 Feb 2023