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.