scholarly journals REFINED SWAN CONDUCTORS OF ONE-DIMENSIONAL GALOIS REPRESENTATIONS

2019 ◽  
Vol 236 ◽  
pp. 134-182
Author(s):  
KAZUYA KATO ◽  
ISABEL LEAL ◽  
TAKESHI SAITO
Keyword(s):  
Field Theory ◽  
Galois Group ◽  
Galois Representations ◽  
Class Field Theory ◽  
Absolute Galois Group ◽  
Class Field ◽  
One Dimensional ◽  
Swan Conductor ◽  
Higher Dimensional ◽  
Valuation Field

For a character of the absolute Galois group of a complete discrete valuation field, we define a lifting of the refined Swan conductor, using higher dimensional class field theory.

The rational characterization of certain sets of relatively Abelian extensions

1959 ◽  
Vol 251 (998) ◽  
pp. 385-425 ◽  
Keyword(s):  
Field Theory ◽  
Galois Group ◽  
Class Group ◽  
Class Field Theory ◽  
Abelian Extension ◽  
Galois Groups ◽  
Class Field ◽  
Abelian Extensions ◽  
Rational Field

Let H be a class group— in the sense of class-field theory— in the rational field P, whose order is some power of a prime l . With H there is associated an Abelian extension K of P. The purpose of this paper is to determine in rational terms and for all fields K given in the described manner, the set T(K/P) of cyclic extensions A of K of relative degree l , which are absolutely normal. In particular we shall find the ramification laws for these fields A, and the possible extension types of a group of order l by the Galois group of K, which are realized in Galois groups of fields in T(K/P). It is fundamental to the programme outlined, that we aim at obtaining purely rational criteria of determination.

scholarly journals Coincidence of two Swan conductors of abelian characters

2019 ◽  
Vol Volume 3 ◽  
Author(s):  
Kazuya Kato ◽  
Takeshi Saito
Keyword(s):  
Galois Group ◽  
Absolute Galois Group ◽  
Swan Conductor ◽  
Valuation Field ◽  
The Absolute

There are two ways to define the Swan conductor of an abelian character of the absolute Galois group of a complete discrete valuation field. We prove that these two Swan conductors coincide. Comment: 16 pages. Formatted using epigamath.sty

scholarly journals HIGHER IDELES AND CLASS FIELD THEORY

2018 ◽  
Vol 236 ◽  
pp. 214-250 ◽  
Author(s):  
MORITZ KERZ ◽  
YIGENG ZHAO
Keyword(s):  
Field Theory ◽  
Class Field Theory ◽  
Duality Theorems ◽  
Class Field ◽  
Higher Dimensional ◽  
Universal Approach

We use higher ideles and duality theorems to develop a universal approach to higher dimensional class field theory.

The Nakayama Map and Ramification for Maximally Complete Fields

1974 ◽  
Vol 26 (4) ◽  
pp. 917-919
Author(s):  
Murray A. Marshall
Keyword(s):  
Field Theory ◽  
Galois Group ◽  
Galois Extension ◽  
Class Field Theory ◽  
Cyclic Extension ◽  
Class Field ◽  
Valued Field ◽  
Group Quotient ◽  
Local Class Field Theory

Let K be a maximally complete valued field and let L be a totally ramified Galois extension of K with Galois group G. Assume (i) the value group quotient of L|K is cyclic and (ii) there exists an unramified cyclic extension of K of the same degree as L. Then there is an isomorphism of Ga onto a subgroup A/N(L×) of K×/N(L×) which maps the ramification group Gi onto AiN(L×)/N(L×) for all i > 0 where Ai = {x ∊ A|v(x ‒ 1) ≧ i}. This generalizes certain results of Local Class Field Theory.

scholarly journals Covering data and higher dimensional global class field theory

2009 ◽  
Vol 129 (10) ◽  
pp. 2569-2599 ◽  
Author(s):  
Moritz Kerz ◽  
Alexander Schmidt
Keyword(s):  
Field Theory ◽  
Class Field Theory ◽  
Class Field ◽  
Higher Dimensional
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