Title: p-converse theorem for elliptic curves with complex multiplication
Speaker: Prof. Ye Tian (MCM)
Time: 2018-4-25, 9:30-11:00
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.
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