Heegner Point Kolyvagin System and Iwasawa Main Conjecture

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.

arXiv comment13 Pages. Comments welcome

Cited by in corpus (9)

• On the non-triviality of the $p$-adic Abel-Jacobi image of generalised Heegner cycles modulo $p$, II: Shimura curves
• A proof of Perrin-Riou's Heegner point main conjecture
• On the Iwasawa main conjectures for modular forms at non-ordinary primes
• Iwasawa Main Conjecture for Rankin-Selberg $p$-adic $L$-functions: Non-Ordinary Case
• On the p-adic Birch and Swinnerton-Dyer conjecture for elliptic curves over number fields
• Anticyclotomic p-ordinary Iwasawa Theory of Elliptic Modular Forms
• $p$-adic heights of Heegner points and Beilinson-Flach elements
• On Howard's main conjecture and the Heegner point Kolyvagin system
• Indivisibility of Heegner points and arithmetic applications