Comparison of the $\mu$-invariants of an abelian variety and its dual abelian variety

TL;DR

This paper compares the Iwasawa -invariants of an abelian variety and its dual by relating their dual Selmer groups over specific Galois extensions, providing formulas that connect their invariants under isogeny.

Contribution

It introduces a formula relating the -invariants of an abelian variety and its dual Selmer groups over large Galois fields, advancing understanding in Iwasawa theory.

Findings

Derived a formula connecting -invariants of dual Selmer groups

Established relations under natural isogenies

Enhanced understanding of Iwasawa invariants in abelian varieties

Abstract

In this note, we compare the dual Selmer groups of an abelian variety with that of its dual over certain large Galois field. We give formula which relates the generalized Iwasawa $\mu$-invariants associated with their dual Selmer groups under the natural isogeny.