Journals / Turkish Journal of Mathematics / 1999 / Cilt: 23 - Sayı: 4
On The Artin Conductor fArtin(c) of a Character c of Gal (E/K) I: Basic Definitions
- Pages
- 519–530
- DOI
- —
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.
Özet
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.