Joint IAS/PU Number Theory Seminar | |

Topic: | A Converse to a Theorem of Gross-Zaqier-Kolyvagin |

Speaker: | Christopher Skinner |

Affiliation: | Princeton University; Member, School of Mathematics |

Date: | Thursday, April 4 |

Time/Room: | 4:30pm - 5:30pm/S-101 |

The theorem of the title is that if the L-function L(E,s) of an elliptic curve E over the rationals vanishes to order r=0 or 1 at s=1 then the rank of the group of rational rational points of E equals r and the Tate-Shafarevich group of E is finite. This talk will describe an approach to the converse. The methods are mostly p-adic.