  We study the Iwasawa theory of a CM elliptic curve $E$ in the anticyclotomic
$\mathbf{Z}_p$-extension $D_\infty$ 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 $D_\infty/K$.

Number Theory;Algebraic Geometry