The main conjecture of Iwasawa theory for elliptic curves with complex multiplication over abelian extensions at supersingular primes

Abstract

Let E be an elliptic curve over an abelian extension F of an imaginary quadratic field K with complex multiplication by K. Let p be a prime number inert over K/Q (i.e. supersingular for E). We prove the main conjecture of Iwasawa theory for p under certain conditions on p. In other words, we prove that the characteristic ideal of the Pontryagin dual of the plus/minus Selmer group of E over the cyclotomic Zp-extension of F is generated by the plus/minus p-adic L-function of E. 2000 Mathematics Subject Classification Primary 11G05, 11R23; Secondary 11G40.