On the equivariant and the non-equivariant main conjecture for imaginary quadratic fields

The Iwasawa main conjecture fields has been an important tool to study the arithmetic of special values of \(L\)-functions of Hecke characters of imaginary quadratic fields. To obtain the finest possible invariants it is important to know the main conjecture for all prime numbers \(p\) and also to h...

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Bibliographic Details
Published in:arXiv.org 2009-08
Main Authors: Johnson-Leung, Jennifer, Kings, Guido
Format: Article
Language:English
Subjects:
Invariants
Prime numbers
Online Access:Get full text
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Summary:The Iwasawa main conjecture fields has been an important tool to study the arithmetic of special values of \(L\)-functions of Hecke characters of imaginary quadratic fields. To obtain the finest possible invariants it is important to know the main conjecture for all prime numbers \(p\) and also to have an equivariant version at disposal. In this paper we first prove the main conjecture for imaginary quadratic fields for all prime numbers \(p\), improving earlier results by Rubin. From this we deduce the equivariant main conjecture in the case that a certain \(\mu\)-invariant vanishes. For prime numbers \(p\nmid 6\) which split in \(K\), this is a theorem by a result of Gillard.
ISSN:2331-8422