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arXiv · 1407.1099

Indivisibility of Heegner points in the multiplicative case

Christopher Skinner·Wei Zhang
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Abstract

For certain elliptic curves $E$ over $\mathbb{Q}$ with multiplicative reduction at a prime $p\geq 5$, we prove the $p$-indivisibility of the derived Heegner classes defined with respect to an imaginary quadratic field $K$, as conjectured by Kolyvagin. The conditions on $E$ include that $E[p]$ be irreducible and not finite at $p$ and that $p$ split in the imaginary quadratic field $K$, along with certain $p$-indivisibility conditions on various Tamagawa factors. The proof extends the arguments of the second author for the case where $E$ has good ordinary reduction at~$p$.

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Christopher Skinner, Wei Zhang. 2014-07-04. Indivisibility of Heegner points in the multiplicative case. https://arxiv.org/abs/1407.1099

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