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L. Papadogiannis:
"Class Field Theory - Artin Reciprocity Law";
Betreuer/in(nen): M. Drmota; Institut für Diskrete Mathematik und Geometrie, 2020; Abschlussprüfung: 11/2020.

In this Thesis we give an introduction in Class Field Theory, provingArtin reciprocity law. The goal of class field theory is to describe the Galois extensions of a local or global field in terms of the arithmetic of the field itself. Apart from a few remarks about the more general cases, these notes will concentrate on the case of abelian extensions, which is the basic case. We give the framework of the theory
introducing Abstract class field theory and we can see how this can
be translated in the case of global class field theory using idele class groups as modules or multiplicative groups in the case of local class field theory. The language that we use is purely algebraic, with the exception of an analytic approach which is mostly redundant nowadays after much effort of the pioneers in that field to confront such a defect, as it was considered.