On the growth of $\mu$-invariant in Iwasawa theory of supersingular Elliptic curves

TL;DR

This paper investigates how the $-invariant behaves in the Iwasawa theory of supersingular elliptic curves when extending from cyclotomic to ^2$-extensions over imaginary quadratic fields, linking it to conjectures about invariance.

Contribution

It establishes a relation between the -invariants of dual plus and minus Selmer groups in higher extensions and shows their invariance is equivalent to the supersingular _M_H(G)-conjecture.

Findings

-invariants relate across extension levels.

Invariance of -invariants characterizes the supersingular _M_H(G)-conjecture.

The paper extends understanding of Selmer groups in non-cyclotomic towers.

Abstract

In this article, we provide a relation between the $\mu$-invariants of the dual plus and minus Selmer groups for supersingular elliptic curves when we ascend from the cyclotomic $\mathbb{Z}_p$-extension to a $\mathbb{Z}_p^2$-extension over an imaginary quadratic field. Furthermore we show that the supersingular $\mathfrak{M}_H(G)$-conjecture is equivalent to the fact that the $\mu$-invariants doesn't change as we go up the tower.