Anticyclotomic Iwasawa theory of CM elliptic curves II

We study the Iwasawa theory of a CM elliptic curve $E$ in the anticyclotomic ${\mathbf{Z}}_p$-extension $D_{\mathrm{\infty }}$ of the CM field $K$, where $p$ is a prime of good, supersingular reduction for $E$. Our main result yields an asymptotic formula for the corank of the $p$-primary Selmer group of $E$ along the extension $D_{\mathrm{\infty }}\mathrm{/}K$.