Iwasawa theory for elliptic curves over imaginary quadratic fields

Let $E$ be an elliptic curve over $mathbb{Q}$, let $K$ be an imaginary quadratic field, and let $K_ infty$ be a $mathbb{Z}_p$-extension of $K$. Given a set $Sigma$ of primes of $K$, containing the primes above $p$, and the primes of bad reduction for $E$, write $K_Sigma$ for the maximal algebraic extension of $K$ which is unramified outside $Sigma$. This paper is devoted to the study of the structure of the cohomology groups $H^i (K_Sigma / K_infty, E_{p^ infty})$ for $i = 1, 2,$ and of the $p$-primary Selmer group Sel$_{p^ infty}(E / K_infty)$, viewed as discrete modules over the Iwasawa algebra of $K_infty / K.$