Functional equations for multi-signed Selmer groups

TL;DR

This paper investigates the functional equations of multi-signed Selmer groups associated with non-ordinary motives with specific Hodge-Tate weights, extending previous results for ordinary motives and supersingular elliptic curves.

Contribution

It generalizes existing functional equation results to a broader class of non-ordinary motives with Hodge-Tate weights 0 and 1.

Findings

Established functional equations for multi-signed Selmer groups of non-ordinary motives

Unified previous results for ordinary motives and supersingular elliptic curves

Extended the scope of Selmer group theory in arithmetic geometry

Abstract

We study the functional equation for the multi-signed Selmer groups for non-ordinary motives whose Hodge-Tate weights are $0$ and $1$, defined by B\"uy\"ukboduk and the first named author. This generalizes simultaneously Greenberg's result for ordinary motives and Kim's result for supersingular elliptic curves.