Self-duality of Selmer groups

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.

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

References in corpus (2)

• Regulator constants and the parity conjecture
• Finding large Selmer rank via an arithmetic theory of local constants

Cited by in corpus (8)

• Regulator constants and the parity conjecture
• On the Birch-Swinnerton-Dyer quotients modulo squares
• Root numbers and parity of ranks of elliptic curves
• Notes on the Parity Conjecture
• Parity conjectures for elliptic curves over global fields of positive characteristic
• On the Birch--Swinnerton-Dyer conjecture and Schur indices
• Growth of Selmer rank in nonabelian extensions of number fields
• The $\ell$-parity conjecture over the constant quadratic extension