Journal of the Institute of Mathematics of Jussieu

Table of Contents - 2003 - Volume 2, Issue 01  


MODULES OVER IWASAWA ALGEBRAS

J. Coates a1, P. Schneider a2 and R. Sujatha a3
a1 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)
a2 Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany (pschnei@math.uni-muenster.de)
a3 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India (sujatha@math.tifr.res.in)

Abstract

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

(Received April 27 2002)
(Accepted June 7 2002)


Key Words: Iwasawa algebras; elliptic curves.