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On the Gras Conjecture for Imaginary Quadratic Fields

Published online by Cambridge University Press:  20 November 2018

Hassan Oukhaba  and
Stéphane Viguié
Hassan Oukhaba
Affiliation:
Laboratoire de mathématique, 16 Route de Gray, 25030 Besançon cedex, France e-mail: houkhaba@univ-fcomte.fr; sviguie@univ-fcomte.fr
Stéphane Viguié
Affiliation:
Laboratoire de mathématique, 16 Route de Gray, 25030 Besançon cedex, France e-mail: houkhaba@univ-fcomte.fr; sviguie@univ-fcomte.fr
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Abstract

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In this paper we extend K. Rubin's methods to prove the Gras conjecture for abelian extensions of a given imaginary quadratic field $k$ and prime numbers $p$ that divide the number of roots of unity in $k$.

Keywords

11R2711R2911G16elliptic unitsStark unitsGras conjectureEuler systems
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 1 , 01 March 2013 , pp. 148 - 160
Copyright
Copyright © Canadian Mathematical Society 2013

References

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