Turkish Journal of Mathematics
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 $\frak f_{\rm Artin}(\chi_\rho)$ of a character $\chi_\rho$ associated to a representation $\rho:\mbox{Gal}(E/K)\rightarrow GL(V)$ of $\mbox{Gal}(E/K)$ with metabelian kernel $\mbox{ker}(\rho)$. 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 $\frak f_{\rm Artin}(\chi_\rho)$ under a suitable assumption.
First Page
519
Last Page
530
Recommended Citation
İKEDA, KAZIM İLHAN (1999) "On The Artin Conductor f_{Artin}(\chi) of a Character \chi of Gal (E/K) I: Basic Definitions," Turkish Journal of Mathematics: Vol. 23: No. 4, Article 4. Available at: https://journals.tubitak.gov.tr/math/vol23/iss4/4
