  Let $E/\mathbb{Q}$ be an elliptic curve, $p$ a prime and $K_{\infty}/K$ the
anticyclotomic $\mathbb{Z}_p$-extension of a quadratic imaginary field $K$
satisfying the Heegner hypothesis. In this paper we give a new proof to a
theorem of Bertolini which determines the value of the $\Lambda$-corank of
$\text{Sel}(E/K_{\infty})$ in the case where $E$ has ordinary reduction at $p$.
In the case where $E$ has supersingular reduction at $p$ we make a conjecture
about the structure of the module of Heegner points mod $p$. Assuming this
conjecture we give a new proof to a theorem of Ciperiani which determines the
value of the $\Lambda$-corank of $\text{Sel}(E/K_{\infty})$ in the case where
$E$ has supersingular reduction at $p$.
