The authors prove Perrin-Riou's Heegner point main conjecture for elliptic curves over the rationals under mild hypotheses, and also prove the Iwasawa-Greenberg main conjecture for Bertolini-Darmon-Prasanna p-adic L-functions.
Heegner Point Kolyvagin System and Iwasawa Main Conjecture
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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.
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2019 1verdicts
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A proof of Perrin-Riou's Heegner point main conjecture
The authors prove Perrin-Riou's Heegner point main conjecture for elliptic curves over the rationals under mild hypotheses, and also prove the Iwasawa-Greenberg main conjecture for Bertolini-Darmon-Prasanna p-adic L-functions.