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Truncated Euler Systems over Imaginary Quadratic Fields

Published online by Cambridge University Press:  11 January 2016

Soogil Seo
Soogil Seo*
Affiliation:
Department of MathematicsYonsei University, 134 Sinchon-Dong Seodaemun-Gu Seoul 120-749, South [email protected]
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Abstract

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Let K be an imaginary quadratic field and let F be an abelian extension of K. It is known that the order of the class group ClF of F is equal to the order of the quotient UF/ElF of the group of global units UF by the group of elliptic units ElF of F. We introduce a filtration on UF/ElF made from the so-called truncated Euler systems and conjecture that the associated graded module is isomorphic, as a Galois module, to the class group. We provide evidence for the conjecture using Iwasawa theory.

Keywords

11R2311R2711R29
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 195 , 2009 , pp. 97 - 111
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

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