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On the Gras Conjecture for Imaginary Quadratic Fields

  Published:2011-08-25
 Printed: Mar 2013
  • Hassan Oukhaba,
    Laboratoire de mathématique, 16 Route de Gray, 25030 Besançon cedex, France
  • Stéphane Viguié,
    Laboratoire de mathématique, 16 Route de Gray, 25030 Besançon cedex, France
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Abstract

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: elliptic units, Stark units, Gras conjecture, Euler systems elliptic units, Stark units, Gras conjecture, Euler systems
MSC Classifications: 11R27, 11R29, 11G16 show english descriptions Units and factorization
Class numbers, class groups, discriminants
Elliptic and modular units [See also 11R27]
11R27 - Units and factorization
11R29 - Class numbers, class groups, discriminants
11G16 - Elliptic and modular units [See also 11R27]
 

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