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The Capitulation Problem in Class Field Theory

Das Kapitulationsproblem in der Klassenkörpertheorie

by Tobias Bembom
Doctoral thesis
Date of Examination:2012-04-02
Date of issue:2012-04-10
Advisor:Prof. Dr. Preda Mihailescu
Referee:Prof. Dr. Preda Mihailescu
Referee:Prof. Dr. Valentin Blomer
crossref-logoPersistent Address: http://dx.doi.org/10.53846/goediss-2521

 

 

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Abstract

English

We develop Chevalley's Theorem and interesting implications. Revisiting Galois Cohomology we analyse the structure of the capitulation kernel. Moreover investigate the growth of ideal classes and consequences of a G-action on the class group. Finally we discuss capitulation in imaginary quadratic fields.
Keywords: Algebraic number theory; class field theory; capitulation

Other Languages

Das Kapitulationsproblem in der Klassenkörpertheorie. Wir entwickeln den Satz von Chevalley mit Implikationen, analysieren mit Hilfe von Galoiskohomologie die Struktur des Kerns. Zudem untersuchen wir das Wachstum von Idealklassen und die Auswirkung einer G-Wirkung auf die Klassengruppe. Schließlich beleuchten wir Kapitulaton in imaginär quadratischen Körpern.
Schlagwörter: Algebraische Zahlentheorie; Klassenkörpertheorie; Kapitulation
 

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