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

 Joint IAS/Princeton University Number Theory Seminar Topic: A converse theorem of Gross-Zagier and Kolyvagin: CM case Speaker: Ye Tian Affiliation: Chinese Academy of Sciences Date: Thursday, October 26 Time/Room: 4:30pm - 5:30pm/S-101 Video Link: https://video.ias.edu/puias/2017/1026-YeTian

Let $E$ be a CM elliptic curves over rationals and $p$ an odd prime ordinary for $E$. If the $\mathbb Z_p$ 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.