On the structure of fine Mordell-Weil groups over a $\mathbb{Z}_p$-extension and its intermediate subextensions

TL;DR

This paper studies the detailed structure of fine Mordell-Weil groups over intermediate subextensions within a specific $Z_p$-extension of a number field.

Contribution

It provides new insights into the algebraic structure of Mordell-Weil groups over various subextensions of a $Z_p$-extension.

Findings

Characterization of the structure of fine Mordell-Weil groups over intermediate subextensions

Identification of properties influencing the group's structure

Potential implications for Iwasawa theory and arithmetic geometry

Abstract

In this paper, we investigate the structure of the fine Mordell-Weil groups over the intermediate subextensions of a given $\mathbb{Z}_p$-extension $F_\infty$ of $F$.