A converse theorem of Gross-Zagier and Kolyvagin: CM case.

A converse theorem of Gross-Zagier and Kolyvagin: CM case.

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Ye Tian, Chinese Academy of Sciences
IAS Room S-101

Let E be a CM elliptic curves over rationals and p an odd prime ordinary for E. If the Z_p corank of p^\infty Selmer group for E equals one, then we show that the analytic rank of E also equals one.This is joint work with Ashay Burungale.