Self-duality of Selmer groups
Number Theory
2013-09-23 v2
Abstract
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.
Cite
@article{arxiv.0705.1899,
title = {Self-duality of Selmer groups},
author = {Tim Dokchitser and Vladimir Dokchitser},
journal= {arXiv preprint arXiv:0705.1899},
year = {2013}
}