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SUMMARY:Pairings and functional equations over the GL_2-extension - Gergel
 y Zabradi (Cambridge)
DTSTART:20080422T133000Z
DTEND:20080422T143000Z
UID:TALK11617@talks.cam.ac.uk
CONTACT:Tim Dokchitser
DESCRIPTION:We construct a pairing on the dual Selmer group over the GL<su
 b>2</sub>-extension Q(E[p<sup>&infin\;</sup>]) of an elliptic curve\nwitho
 ut complex multiplication and with good ordinary reduction at\na prime p&g
 e\;5 whenever it satisfies certain - conjectural\n- torsion properties. Th
 is gives a functional equation of the\ncharacteristic element which is com
 patible with the conjectural\nfunctional equation of the p-adic L-function
 . As an\napplication we reduce the parity conjecture for the p-Selmer\nran
 k and the analytic root number for the twists of elliptic\ncurves with sel
 f-dual Artin representation to the case when the\nArtin representation fac
 tors through the quotient of\nQ(E[p<sup>&infin\;</sup>])/Q by its maximal 
 pro-p normal subgroup.\nThis gives a proof of the parity\nconjecture whene
 ver the curve E has a p-isogeny over the rationals.
LOCATION:MR13
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