|Joint IAS/PU Number Theory Seminar|
|Topic:||A Converse to a Theorem of Gross-Zaqier-Kolyvagin|
|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.