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EULER CHARACTERISTICS AS INVARIANTS OF IWASAWA MODULES

Published online by Cambridge University Press:  14 October 2002

SUSAN HOWSON
SUSAN HOWSON
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD. sh@maths.nott.ac.uk
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Abstract

If $G$ is a pro-$p$, $p$-adic, Lie group containing no element of order $p$ and if $\Lambda (G)$ denotes the Iwasawa algebra of $G$ then we propose a number of invariants associated to finitely generated $\Lambda (G)$-modules, all given by various forms of Euler characteristic. The first turns out to be none other than the rank, and this gives a particularly convenient way of calculating the rank of Iwasawa modules. Others seem to play similar roles to the classical Iwasawa $\lambda $- and $\mu $-invariants. We explore some properties and give applications to the Iwasawa theory of elliptic curves.

2000 Mathematical Subject Classification: primary 16E10; seconday 11R23.

Keywords

Euler characteristicshomological algebra$\mu$-invariantsIwasawa theoryelliptic curves
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 85 , Issue 3 , November 2002 , pp. 634 - 658
Copyright
2002 London Mathematical Society

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