Let A/Q be an elliptic curve having split multiplicative reduction at an odd prime p. Under some mild technical assumptions, we prove the statement: (equation presented) thus providing a 'p-converse' to a celebrated theorem of Kolyvagin-Gross-Zagier.
On the p-converse of the Kolyvagin–Gross–Zagier theorem / R. Venerucci. - In: COMMENTARII MATHEMATICI HELVETICI. - ISSN 0010-2571. - 91:3(2016), pp. 397-444. [10.4171/CMH/390]
On the p-converse of the Kolyvagin–Gross–Zagier theorem
R. Venerucci
2016
Abstract
Let A/Q be an elliptic curve having split multiplicative reduction at an odd prime p. Under some mild technical assumptions, we prove the statement: (equation presented) thus providing a 'p-converse' to a celebrated theorem of Kolyvagin-Gross-Zagier.
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