Iwasawa theory for elliptic curves over imaginary quadratic fields

Abstract

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