Heegner Point Kolyvagin System and Iwasawa Main Conjecture

TL;DR

This paper proves an anticyclotomic Iwasawa main conjecture related to Heegner points and Kolyvagin systems, advancing understanding of p-adic L-functions and their associated Selmer groups in number theory.

Contribution

It establishes the main conjecture for Heegner points with global sign -1, utilizing recent work on divisibility of Iwasawa-Greenberg conjectures, and confirms the conjecture's equality under certain conditions.

Findings

Proved the anticyclotomic Iwasawa main conjecture for Heegner points with sign -1.

Established the equality of the main conjecture under local conditions.

Connected the conjecture to recent divisibility results of p-adic L-functions.

Abstract

In this paper we prove an anticyclotomic Iwasawa main conjecture proposed by Perrin-Riou for Heegner points when the global sign is -1, using a recent work of the author on one divisibility of Iwasawa-Greenberg main conjecture for Rankin-Selberg p-adic L-functions. As a byproduct we also prove the equality for the above mentioned main conjecture under some local conditions.