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

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

Ye Tian
Chinese Academy of Sciences
October 26, 2017
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.