Joint IAS/PU Number Theory Seminar

Submitted by admin on Mon, 03/25/2013 - 15:01
A Converse to a Theorem of Gross-Zaqier-Kolyvagin
Christopher Skinner
Princeton University; Member, School of Mathematics
Date & Time: 
Thu, 04/04/2013 - 16:30 - 17:30
Location: 
S-101
Video Link: 

http://video.ias.edu/jointiaspu/1213/0404-ChristopherSkinner

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.

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