a1 Robinson College, Cambridge CB39AN. e-mail: email@example.com
a2 Gonville & Caius College, Cambridge CB21TA. e-mail: firstname.lastname@example.org
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 G-representation naturally associated to the p∞-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.
(Received May 11 2008)
† Supported by a Royal Society University Research Fellowship.