Speaker: Prof. Ye Tian (MCM)

Title: p-converse theorem for elliptic curves with complex multiplication

Time: 9:30, April 25, 2018

Place: N818

Abstract: Let E be an elliptic curve defined over rationals and p a prime. A theorem of Gross-Zagier and Kolyvagin says that if the L-function of E has vanishing order one at the center then the corank of its p-Selmer group is also one. In a joint work with Burungale, we show the converse to the above result in the case that E has complex multiplication and p>3 is ordinary for E. We will introduce the related concepts via the congruent number problem.