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

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.