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

Burungale, Ashay and Castella, Francesc and Kim, Chan-Ho (2021) A proof of Perrin-Riou's Heegner point main conjecture. Algebra & Number Theory, 15 (7). pp. 1627-1653. ISSN 1944-7833. doi:10.2140/ant.2021.15.1627. https://resolver.caltech.edu/CaltechAUTHORS:20211130-203141758

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.2140/ant.2021.15.1627DOIArticle
https://arxiv.org/abs/1908.09512arXivDiscussion Paper
ORCID:
AuthorORCID
Burungale, Ashay0000-0002-2469-2115
Castella, Francesc0000-0002-5532-2387
Kim, Chan-Ho0000-0002-5932-9391
Additional Information:© 2021 Mathematical Sciences Publishers. Received: 28 August 2019; Revised: 4 September 2020; Accepted: 12 October 2020; Published: 1 November 2021.
Issue or Number:7
Classification Code:2010 Mathematics Subject Classification: 11R23 (Primary); 11F33 (Secondary).
DOI:10.2140/ant.2021.15.1627
Record Number:CaltechAUTHORS:20211130-203141758
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20211130-203141758
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112092
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:30 Nov 2021 21:25
Last Modified:30 Nov 2021 21:25

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