Number Theory Seminar

Tuesday 5 June 2007, MR13, 2:30

Parity Conjecture for elliptic curves over Q
Vladimir Dokchitser (Cambridge)


     For an elliptic curve E over a number field K, various "modulo 2" versions of the Birch-Swinnerton-Dyer Conjecture relate the parities of the Mordell-Weil rank, analytic rank and p-Selmer ranks. The aim of this talk is to prove that over Q the parity of every p-Selmer rank agrees with the parity of the analytic rank (completing earlier work by Greenberg, Guo, Monsky, Nekovar and Kim). A key ingredient is a "local-to-global" expression for various combinations of ranks of E over extensions of K, which is motivated by Artin formalism for L-functions. (This is joint work with Tim Dokchitser.)

Last modified on 17/4/2007.

Comments/corrections to Tim Dokchitser