arXiv 0705.18992007-05math.NT

Self-duality of Selmer groups

Tim Dokchitser, Vladimir Dokchitser

备注：: 12 pages; to appear in Proc. Cam. Phil. Soc
发表信息：: Proc. Cam. Phil. Soc. 146 (2009), 257-267
DOI：: 10.1017/S0305004108001989

英文摘要：

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.

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