Abstract
Let be an elliptic curve of conductor , let be a prime where has good ordinary reduction, and let be an imaginary quadratic field satisfying the Heegner hypothesis. In 1987, Perrin-Riou formulated an Iwasawa main conjecture for the Tate–Shafarevich group of over the anticyclotomic -extension of 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 splits in , we also obtain a proof of the Iwasawa–Greenberg main conjecture for the -adic -functions of Bertolini, Darmon and Prasanna.
Citation
Ashay Burungale. Francesc Castella. Chan-Ho Kim. "A proof of Perrin-Riou's Heegner point main conjecture." Algebra Number Theory 15 (7) 1627 - 1653, 2021. https://doi.org/10.2140/ant.2021.15.1627
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