On the structure of Selmer groups over p p -adic Lie extensions

The goal of this paper is to prove that the Pontryagin dual of the Selmer group over the trivializing extension of an elliptic curve without complex multiplication does not have any nonzero pseudo-null submodule. The main point is to extend the definition of pseudo-null to modules over the completed...

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Bibliographic Details
Published in:Journal of algebraic geometry 2002-03, Vol.11 (3), p.547-580
Main Authors: Ochi, Yoshihiro, Venjakob, Otmar
Format: Article
Language:English
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Research article
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Summary:The goal of this paper is to prove that the Pontryagin dual of the Selmer group over the trivializing extension of an elliptic curve without complex multiplication does not have any nonzero pseudo-null submodule. The main point is to extend the definition of pseudo-null to modules over the completed group ring Zp[[G]]\mathbb {Z}_p[[G]] of an arbitrary pp-adic Lie group GG without pp-torsion. For this purpose we prove that Zp[[G]]\mathbb {Z}_p[[G]] is an Auslander regular ring. For the proof we also extend some results of Jannsen’s homotopy theory of modules and study intensively higher Iwasawa adjoints.
ISSN:1056-3911
1534-7486
DOI:10.1090/S1056-3911-02-00297-7