Iwasawa Main Conjecture for Heegner Points: Supersingular Case

Abstract

In this paper we propose and prove an anticyclotomic Iwasawa main conjecture for Heegner points on supersingular elliptic curves with $a_p=0$. The result has a "$\pm$" nature in the sense of Kobayashi. The proof uses a recent work of the second author on one divisibility in the Iwasawa--Greenberg main conjecture for Rankin-Selberg $p$-adic $L$-functions, together with an argument of Howard (adapted to our "$\pm$"-situation). As a byproduct, we also obtain an improvement of Skinner's result on a converse to the Gross--Zagier--Kolyvagin theorem.

15 pages. Comments welcome

References in corpus (1)

• Heegner cycles and $p$-adic $L$-functions

Cited by in corpus (3)

• Iwasawa Main Conjecture for Rankin-Selberg $p$-adic $L$-functions: Non-Ordinary Case
• $p$-adic heights of Heegner points and Beilinson-Flach elements
• Kolyvagin's Conjecture and patched Euler systems in anticyclotomic Iwasawa theory