A converse to a theorem of GrossZagierKolyvagin
A converse to a theorem of GrossZagierKolyvagin

Christopher Skinner , Princeton University and IAS
IAS Room S101
The theorem of the title is that if the Lfunction 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 TateShafarevich group of E is finite. This talk will describe an approach to the converse. The methods are mostly padic.