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CENTRES OF SKEWFIELDS AND COMPLETELY FAITHFUL IWASAWA MODULES

Published online by Cambridge University Press:  18 March 2008

Konstantin Ardakov
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK (konstantin.ardakov@nottingham.ac.uk)

Abstract

Let $H$ be a torsion-free compact $p$-adic analytic group whose Lie algebra is split semisimple. We show that the quotient skewfield of fractions of the Iwasawa algebra $\varLambda_H$ of $H$ has trivial centre and use this result to classify the prime $c$-ideals in the Iwasawa algebra $\varLambda_G$ of $G:=H\times\mathbb{Z}_p$. We also show that a finitely generated torsion $\varLambda_G$-module having no non-zero pseudo-null submodule is completely faithful if and only if it is has no central torsion. This has an application to the study of Selmer groups of elliptic curves.

Type
Research Article
Copyright
2008 Cambridge University Press

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