A Converse to a Theorem of Gross-Zaqier-Kolyvagin

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.