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$\Z_p$-extensions associated to elliptic curves with complex multiplication

Published online by Cambridge University Press:  02 November 2004

TAKASHI FUKUDA  and
KEIICHI KOMATSU
TAKASHI FUKUDA
Affiliation:
Department of Mathematics, College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba, Japan. e-mail: [email protected]
KEIICHI KOMATSU
Affiliation:
Department of Mathematical Science, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169, Japan. e-mail: [email protected]
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Abstract

Let $E$ be an elliptic curve defined over $\Q$ with complex multiplication by the ring of integers of an imaginary quadratic field $K$. We apply an elliptic unit version of Ichimura–Sumida criterion for the $\Z_p$-extension $F_\infty/F$ associated to $E$ and try to determine the characteristic polynomial of the maximal unramified abelian $p$-extension of $F_\infty$.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 137 , Issue 3 , November 2004 , pp. 541 - 550
Copyright
© 2004 Cambridge Philosophical Society

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