Iwasawa's Main Conjecture for elliptic curves over Coates-Wiles Z_p-extensions

Abstract

We present Iwasawa theory of elliptic curves with complex multiplication first formulated by Coates and Wiles. As a consequence of the main conjecture, we see that how this result lends some evidence for the classical Birch and Swinnerton-Dyer conjecture. Also, we provide numerical criterion and examples by analyzing the structure of Iwasawa modules. For a certain family of quadratic twists, we compute Iwasawa mu and lambda-invariants which is predicted by Iwasawa theory.