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Annihilators of the Ideal Class Group of a Cyclic Extension of an Imaginary Quadratic Field

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  09 January 2019

Hugo Chapdelaine  and
Radan Kučera
Hugo Chapdelaine
Affiliation:
Faculty of Science and Engineering, Laval University, Québec G1V 0A6, Canada Email: hugo.chapdelaine@mat.ulaval.ca
Radan Kučera
Affiliation:
Faculty of Science, Masaryk University, 611 37 Brno, Czech Republic Email: kucera@math.muni.cz
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Abstract

The aim of this paper is to study the group of elliptic units of a cyclic extension $L$ of an imaginary quadratic field $K$ such that the degree $[L:K]$ is a power of an odd prime $p$. We construct an explicit root of the usual top generator of this group, and we use it to obtain an annihilation result of the $p$-Sylow subgroup of the ideal class group of $L$.

Keywords

annihilatorclass groupelliptic unit

MSC classification

Primary: 11R20: Other abelian and metabelian extensions
Secondary: 11R27: Units and factorization 11R29: Class numbers, class groups, discriminants
Type
Article
Information
Canadian Journal of Mathematics , Volume 71 , Issue 6 , December 2019 , pp. 1395 - 1419
Copyright
© Canadian Mathematical Society 2018 

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Footnotes

The second author was supported under Project 15-15785S of the Czech Science Foundation.

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