Heegner Point Kolyvagin System and Iwasawa Main Conjecture

We prove an anticyclotomic Iwasawa main conjecture proposed by Perrin-Riou for Heegner points semi-stable elliptic curves E over a quadratic imaginary field K satisfying certain generalized hypothesis, at ordinary prime p. It states that the square of index family in equals characteristic ideal torsion part its Bloch-Kato Selmer group (see Theorem 1.3 precise statement). As byproduct we also equality Greenberg-Iwasawa Rankin-Selberg product (Theorem 1.7) under some local conditions, and improvement Skinner’s result on converse Gross-Zagier Kolyvagin theorem (Corollary 1.11).