A converse to a theorem of Gross--Zagier, Kolyvagin and Rubin, II

A converse to a theorem of Gross--Zagier, Kolyvagin and Rubin, II

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Ashay Burungale, IAS
IAS Room S-101

Let E be a CM elliptic curve over a totally real number field F and p an odd ordinary prime. If the p^{\infty}-Selmer group of E over F has \Z_{p}-corank one, we show that the analytic rank of E over F is also one (joint with Chris Skinner and Ye Tian). We plan to discuss the setup and strategy.