... e of J over Z Write JF for the special fiber of J, JF for the connected component of the origin in JF , and Φ = Φ (X) for the group of connected IWASAWA’S MAIN CONJECTURE FOR ELLIPTIC CURVES ... rank #S over Λ/pn Λ IWASAWA’S MAIN CONJECTURE FOR ELLIPTIC CURVES 23 Proof The fact that HS (Km , Tf,n ) is free over Z/pn Z[Gm ] is essentially Theorem 3.2 of [BD0], whose proof carries over, ... 162 (2005), 1–64 Iwasawa’s Main Conjecture for elliptic curves over anticyclotomic Zp-extensions By M Bertolini∗ and H Darmon∗* Contents p-adic L-functions 1.1 Modular forms on quaternion algebras...