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SELMER GROUPS OVER $p$-ADIC LIE EXTENSIONS I

Published online by Cambridge University Press:  03 December 2004

SARAH LIVIA ZERBES
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, United Kingdoms.zerbes@dpmms.cam.ac.uk
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Abstract

Let $E$ be an elliptic curve defined over a number field $F$. The paper concerns the structure of the $p^{\backslash}\infty$-Selmer group of $E$ over $p$-adic Lie extensions $F_{\backslash}\infty$ of $F$ which are obtained by adjoining to $F$ the $p$-division points of an abelian variety $A$ defined over $F$. The main focus of the paper is the calculation of the Gal$(F_{\backslash}\infty/F)$-Euler characteristic of the $p^{\backslash}\infty$-Selmer group of $E$. The main theory is illustrated with the example of an elliptic curve of conductor 294.

Keywords

Type
Notes and Papers
Copyright
The London Mathematical Society 2004

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Footnotes

This research was supported by the EPSRC.