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.