On the -converse of the Kolyvagin–Gross–Zagier theorem

  • Rodolfo Venerucci

    Universität Duisburg-Essen, Germany

Abstract

Let be an elliptic curve having split multiplicative reduction at an odd prime . Under some mild technical assumptions, we prove the statement:

thus providing a ‘-converse’ to a celebrated theorem of Kolyvagin–Gross–Zagier.

Cite this article

Rodolfo Venerucci, On the -converse of the Kolyvagin–Gross–Zagier theorem. Comment. Math. Helv. 91 (2016), no. 3, pp. 397–444

DOI 10.4171/CMH/390