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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Yoshihiro Ochi
Journal: Proc. Amer. Math. Soc. 134 (2006), 31-37
MSC (2000): Primary 11R23, 11G10
Published electronically: August 11, 2005
MathSciNet review: 2170540
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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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Additional Information

Yoshihiro Ochi
Affiliation: School of Science and Engineering, Tokyo Denki University, Tokyo, 101–8457, Japan
Email: ochi@u.dendai.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08292-4
PII: S 0002-9939(05)08292-4
Keywords: Selmer groups, abelian varieties, Iwasawa theory.
Received by editor(s): August 11, 2004
Published electronically: August 11, 2005
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.