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Self-duality of Selmer groups

Published online by Cambridge University Press:  01 March 2009

TIM DOKCHITSER  and
VLADIMIR DOKCHITSER
TIM DOKCHITSER
Affiliation:
Robinson College, Cambridge CB39AN. e-mail: [email protected]
VLADIMIR DOKCHITSER
Affiliation:
Gonville & Caius College, Cambridge CB21TA. e-mail: [email protected]
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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 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 2 , March 2009 , pp. 257 - 267
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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