The growth of Selmer ranks of an Abelian variety with complex multiplication

Let K be a CM field and O be its ring of integers. Let p be an odd prime integer and p be a prime in K lying above p. Let F be a Galois extension of K unramified over p. For an Abelian variety A defined over F with complex multiplication by O, we study the variation of the p-ranks of the Selmer groups in pro-p algebraic extensions. We first study the Z(p)-extension case. When K is quadratic imaginary and E is an elliptic curve, we also study the p-ranks of the Selmer groups in an unramified p-class field tower.