English

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.

Keywords

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}
}
R2 v1 2026-06-21T08:27:58.249Z