Kazım İlhan İKEDA

8168

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

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.

Anahtar Kelimeler:

Turk. J. Math., 23, (1999), 519-530. Full text: pdf Other articles published in the same issue: Turk. J. Math., vol.23, iss.4.

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

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.,

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Arşiv

Sayıdaki Diğer Makaleler

On The Asymptotic Behavior of Heegner Points

The projectivity of the fundamental group of an affine line

Shafarevich-Tate set for $y^4=x^4-ell^4$

The Weight Equations for Binary Linear Codes

Ersan AKYILDIZ, Masatoshi IKEDA, İsmail Ş. GÜLOĞLU

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

Kazım İlhan İKEDA

On the Artin conductor $f_Artin(X)$ of a character $X$ of Gal (E/K) I: Basic definitions

Kazım İlhan IKEDA

A survey on Drinfeld modular forms

Ernst-Ulrich GEKELER

On the asymptotic behaviour of Heegner points

Jan NEKOVAR, Norbert SCHAPPACHER

On generalized Shioda-Inose structures

S. SERTÖZ, H. ÖNSİPER