Cambridge Journal of Mathematics

Volume 2 (2014)

Number 2

Selmer groups and the indivisibility of Heegner points

Pages: 191 – 253

DOI: http://dx.doi.org/10.4310/CJM.2014.v2.n2.a2

Author

Wei Zhang (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Abstract

For elliptic curves over $\mathbb{Q}$, we prove the $p$-indivisibility of derived Heegner points for certain prime numbers $p$, as conjectured by Kolyvagin in 1991. Applications include the refined Birch-Swinerton-Dyer conjecture in the analytic rank one case, and a converse to the theorem of Gross-Zagier and Kolyvagin. A slightly different version of the converse is also proved earlier by Skinner.

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