Higher codimension Iwasawa theory for elliptic curves with supersingular reduction

TL;DR

This paper generalizes higher codimension Iwasawa theory for elliptic curves with supersingular reduction, extending previous work by Lei, Palvannan, and Bleher et al., using advanced techniques involving Selmer groups and norm subgroups.

Contribution

It provides a broad generalization of existing results in higher codimension Iwasawa theory for supersingular elliptic curves, introducing new structural insights.

Findings

Extended the framework of Lei and Palvannan to more general settings.

Analyzed the structure of $ ext{±}$-norm subgroups and duality in Selmer groups.

Developed a novel approach based on Bleher et al.'s work.

Abstract

Bleher et al. began studying higher codimension Iwasawa theory for classical Iwasawa modules. Subsequently, Lei and Palvannan studied an analogue for elliptic curves with supersingular reduction. In this paper, we obtain a vast generalization of the work of Lei and Palvannan. A key technique is an approach to the work of Bleher et al. that the author previously proposed. For this purpose, we also study the structure of $\pm$-norm subgroups and duality properties of multiply-signed Selmer groups.