On the growth of $\mu $-invariant in Iwasawa theory of supersingular elliptic curves
Volume 202 / 2022
Acta Arithmetica 202 (2022), 241-251
MSC: Primary: 11R23, 11G05.
DOI: 10.4064/aa200724-11-7
Published online: 9 February 2022
Abstract
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 statement that the $\mu $-invariant does not change as we go up the tower.
