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.

Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.