Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



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

Authors: Yoshihiro Ochi and Otmar Venjakob
Journal: J. Algebraic Geom. 11 (2002), 547-580
Published electronically: March 18, 2002
MathSciNet review: 1894938
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Abstract | References | Additional Information

Abstract: 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 $\mathbb{Z} _p[[G]]$ of an arbitrary $p$-adic Lie group $G$ without $p$-torsion. For this purpose we prove that $\mathbb{Z} _p[[G]]$ 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.

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Additional Information

Yoshihiro Ochi
Affiliation: Universität Heidelberg, Mathematisches Institut, Im Neuenheimer Feld 288, 69120 Heidelberg, Germany
Address at time of publication: Korea Institute for Advanced Study (KIAS), 207-43 Cheongryangri-dong, Dongdaemun-gu, Seoul 130-012, South Korea

Otmar Venjakob
Affiliation: Universität Heidelberg, Mathematisches Institut, Im Neuenheimer Feld 288, 69120 Heidelberg, Germany
Address at time of publication: Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 OWB, United Kingdom

Received by editor(s): May 14, 2000
Received by editor(s) in revised form: September 6, 2000
Published electronically: March 18, 2002
Additional Notes: During this research, Y. Ochi has been supported by the Deutsche Forschungsgemeinschaft (DFG) “Forschergruppe Arithmetik" at the Mathematical Institute, Heidelberg.

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