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Gergely Zabradi (Cambridge)
Tuesday 22 April 2008, 14:30-15:30
Pairings and functional equations over the GL_2-extension
- đ¤ Speaker: Gergely Zabradi (Cambridge)
- đ Date & Time: Tuesday 22 April 2008, 14:30 - 15:30
- đ Venue: MR13
Abstract
We construct a pairing on the dual Selmer group over the GL2-extension Q(E[p∞]) of an elliptic curve without complex multiplication and with good ordinary reduction at a prime p≥5 whenever it satisfies certain – conjectural - torsion properties. This gives a functional equation of the characteristic element which is compatible with the conjectural functional equation of the p-adic L-function. As an application we reduce the parity conjecture for the p-Selmer rank and the analytic root number for the twists of elliptic curves with self-dual Artin representation to the case when the Artin representation factors through the quotient of Q(E[p∞])/Q by its maximal pro-p normal subgroup. This gives a proof of the parity conjecture whenever the curve E has a p-isogeny over the rationals.
Series This talk is part of the Number Theory Seminar series.
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