On The Artin Conductor fArtin(c) of a Character c of Gal (E/K) I: Basic Definitions

Authors : Kazım Ilhan Ikeda

Pages : 519-530

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Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :Let K be a local field with finite residue class field and E a finite Galois extension over K. In this paper, we study the Artin conductor \frak f\rm Artin(c\rho) of a character c\rho associated to a representation r:\mbox{Gal}(E/K)\rightarrow GL(V) of \mbox{Gal}(E/K) with metabelian kernel \mbox{ker}(r). In order to do so, we first review the Artin character a\mbox{Gal}(E/K) of \mbox{Gal}(E/K) and review the metabelian local class field theory. We finally propose the definition of the conductor \frak f(E/K) of a metabelian extension E/K in the sense of Koch-de Shalit local class field theory, and compute \frak f\rm Artin(c\rho) under a suitable assumption.
Keywords : Turk. J. Math., 23, (1999), 519-530. Full text: pdf Other articles published in the same issue: Turk. J. Math., vol.23, iss.4.