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Published November 2, 2021 | Accepted Version
Journal Article Open

A proof of Perrin-Riou's Heegner point main conjecture


Let E∕Q be an elliptic curve of conductor N, let p > 3 be a prime where E has good ordinary reduction, and let K be an imaginary quadratic field satisfying the Heegner hypothesis. In 1987, Perrin-Riou formulated an Iwasawa main conjecture for the Tate–Shafarevich group of E over the anticyclotomic Zp-extension of K in terms of Heegner points. In this paper, we give a proof of Perrin-Riou's conjecture under mild hypotheses. Our proof builds on Howard's theory of bipartite Euler systems and Wei Zhang's work on Kolyvagin's conjecture. In the case when p splits in K, we also obtain a proof of the Iwasawa–Greenberg main conjecture for the p-adic L-functions of Bertolini, Darmon and Prasanna.

Additional Information

© 2021 Mathematical Sciences Publishers. Received: 28 August 2019; Revised: 4 September 2020; Accepted: 12 October 2020; Published: 1 November 2021.

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August 22, 2023
October 23, 2023