Self-duality of Selmer groups

Details Self-duality of Selmer groups Self-duality of Selmer groups

2007-05-14

arxiv.org/abs/0705.1899v2

Mathematics

Number Theory

12 pages; to appear in Proc. Cam. Phil. Soc

Scientific paper

10.1017/S0305004108001989

The first part of the paper gives a new proof of self-duality for Selmer groups: if A is an abelian variety over a number field K, and F/K is a Galois extension with Galois group G, then the Q_pG-representation naturally associated to the p-infinity Selmer group of A/F is self-dual. The second part describes a method for obtaining information about parities of Selmer ranks from the local Tamagawa numbers of A in intermediate extensions of F/K.

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