Indivisibility of Heegner points in the multiplicative case

2014/07/04 by Skinner, Christopher, Zhang, Wei · 1 citation
#11F67 #11G05 #11G40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1407.1099

Abstract

For certain elliptic curves E over ℚ with multiplicative reduction at a prime p≥ 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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