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

Authors : Kazım İlhan İKEDA

Pages : 519-530

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Publication Date : 0000-00-00

Article Type : Research Paper

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 Artininsert ignore into journalissuearticles values(c\rho); of a character c\rho associated to a representation r:\mbox{Gal}insert ignore into journalissuearticles values(E/K);\rightarrow GLinsert ignore into journalissuearticles values(V); of \mbox{Gal}insert ignore into journalissuearticles values(E/K); with metabelian kernel \mbox{ker}insert ignore into journalissuearticles values(r);. In order to do so, we first review the Artin character a\mbox{Gal}insert ignore into journalissuearticles values(E/K); of \mbox{Gal}insert ignore into journalissuearticles values(E/K); and review the metabelian local class field theory. We finally propose the definition of the conductor \frak finsert ignore into journalissuearticles values(E/K); of a metabelian extension E/K in the sense of Koch-de Shalit local class field theory, and compute \frak f\rm Artininsert ignore into journalissuearticles values(c\rho); under a suitable assumption.
Keywords : Turk J Math, 23, 1999, , 519 530 Turk J Math, vol 23, iss 4