Heegner Point Kolyvagin System and Iwasawa Main Conjecture  

作　　者：Xin WAN 

机构地区：[1]Academy of Mathematics and Systems Science,Chinese Academy of Science and University of Chinese Academy of Science,Beijing 100190,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第1期104-120,共17页数学学报（英文版）

基　　金：the Chinese Academy of Science(Grant No.Y729025EE1);NSFC(Grant Nos.11688101,11621061);an NSFC grant associated to the recruitment Program of Global Experts。

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

关 键 词：Iwasawa theory Heegner Kolyvagin 

分 类 号：O186.11[理学—数学]