The paper upgrades Howard's divisibility to the full Howard main conjecture when the Heegner-point Kolyvagin system is primitive, and shows the conjecture is equivalent to primitivity plus a Tamagawa-factor condition.
Indivisibility of Heegner points and arithmetic applications
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abstract
We upgrade Howard's divisibility towards Perrin-Riou's Heegner point main conjecture to the predicted equality. Contrary to previous works in this direction, our main result allows for the classical Heegner hypothesis and non-squarefree conductors. The main ingredients we exploit are W.~Zhang's proof of Kolyvagin's conjecture, Kolyvagin's structure theorem for Shafarevich--Tate groups, and the explicit reciprocity law for Heegner points.
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2019 1verdicts
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On Howard's main conjecture and the Heegner point Kolyvagin system
The paper upgrades Howard's divisibility to the full Howard main conjecture when the Heegner-point Kolyvagin system is primitive, and shows the conjecture is equivalent to primitivity plus a Tamagawa-factor condition.