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MODULES OVER IWASAWA ALGEBRAS

Published online by Cambridge University Press:  27 January 2003

J. Coates ,
P. Schneider  and
R. Sujatha
J. Coates
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Centre for Mathematical Science, Wilberforce Road, Cambridge CB3 0WB, UK (j.h.coates@dpmms.cam.ac.uk)
P. Schneider
Affiliation:
Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany (pschnei@math.uni-muenster.de)
R. Sujatha
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India (sujatha@math.tifr.res.in)
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Abstract

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Let $G$ be a compact $p$-valued $p$-adic Lie group, and let $\varLambda(G)$ be its Iwasawa algebra. The present paper establishes results about the structure theory of finitely generated torsion $\varLambda(G)$-modules, up to pseudo-isomorphism, which are largely parallel to the classical theory when $G$ is abelian (except for basic differences which occur for those torsion modules which do not possess a non-zero global annihilator). We illustrate our general theory by concrete examples of such modules arising from the Iwasawa theory of elliptic curves without complex multiplication over the field generated by all of their $p$-power torsion points.

AMS 2000 Mathematics subject classification: Primary 11G05; 11R23; 16D70; 16E65; 16W70

Keywords

Iwasawa algebraselliptic curves
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 2 , Issue 1 , January 2003 , pp. 73 - 108
Copyright
2003 Cambridge University Press