A note on Selmer groups of abelian varieties over the trivializing extensions

Ochi, Yoshihiro

doi:10.1090/S0002-9939-05-08292-4

A note on Selmer groups of abelian varieties over the trivializing extensions
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Proc. Amer. Math. Soc. 134 (2006), 31-37 Request permission

Abstract:

We prove that for any abelian variety $A$ defined over a number field $K$ that is not isogenous to a product of CM elliptic curves, the pontrjagin dual of the Selmer group of the abelian variety over the trivializing extension $K(A[p^\infty ])$ has no nonzero pseudo-null submodules.

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