Elliptic Curves, Quadratic Twists and p-(in)divisibility of L-Values

IAS/PRINCETON NUMBER THEORY SEMINAR
Topic:Elliptic Curves, Quadratic Twists and p-(in)divisibility of L-Values
Speaker:Kartik Prasanna
Affiliation:University of California, Los Angeles
Date:Monday, November 28
Time/Room:2:00pm - 3:00pm/Princeton University, Fine Hall 224

Let E be an elliptic curve over the rationals and p a fixed prime. A (very hard) question of Kolyvagin asks if there exists a quadratic discriminant d such that the Tate-Shafarevich group of the quadratic twist E_d has order prime to p. I will explain some recent results that are related to this question, that are obtained by studying the p-adic properties of the Shimura correspondence.