• Corpus ID: 119179041

On Abelianized Absolute Galois Group of Global Function Fields

@article{Smit2017OnAA,
title={On Abelianized Absolute Galois Group of Global Function Fields},
author={Bart de Smit and Pavel Solomatin},
journal={arXiv: Number Theory},
year={2017}
}
• Published 16 March 2017
• Mathematics
• arXiv: Number Theory
The main purpose of this paper is to describe the abelian part $\mathcal G^{ab}_{K}$ of the absolute Galois group of a global function field $K$ as pro-finite group. We will show that the characteristic $p$ of $K$ and the non $p$-part of the class group of $K$ are determined by $\mathcal G^{ab}_{K}$. The converse is almost true: isomorphism type of $\mathcal G_K^{ab}$ as pro-finite group is determined by the invariant $d_K$ of the constant field $\mathbb F_q$ introduced in first section and the…
1 Citations
A remark On Abelianized Absolute Galois Group of Imaginary Quadratic Fields
• Mathematics
• 2017
The main purpose of this paper is to extend results on isomorphism types of the abelianized absolute Galois group $\mathcal G_K^{ab}$, where $K$ denotes imaginary quadratic field. In particular, we

References

SHOWING 1-10 OF 13 REFERENCES
Imaginary quadratic fields with isomorphic abelian Galois groups
• Mathematics
• 2012
In 1976, Onabe discovered that, in contrast to the Neukirch-Uchida results that were proved around the same time, a number field $K$ is not completely characterized by its absolute abelian Galois
Two-torsion in the Jacobian of hyperelliptic curves over finite fields
Abstract. We determine the exact dimension of the $${\bf{F}}_2$$-vector space of $${\bf{F}}_q$$-rational 2-torsion points in the Jacobian of a hyperelliptic curve over $${\bf{F}}_q$$ (q odd) in
Isomorphisms of Galois Groups of Algebraic Function Fields
THEOREM. If there exists a topological isomorphism v: G1 G2, there corresponds a unique isomorphism of fields z: Q, I Q2 such that U(gJ = rgl 1 for every g, e G1. An analogous theorem for algebraic
Number Theory in Function Fields
Polynomials over Finite Fields.- Primes, Arithmetic Functions, and the Zeta Function.- The Reciprocity Law.- Dirichlet L-series and Primes in an Arithmetic Progression.- Algebraic Function Fields and
Pontryagin Duality and the Structure of Locally Compact Abelian Groups
1. Introduction to topological groups 2. Subgroups and quotient groups of Rn 3. Uniform spaces and dual groups 4. Introduction to the Pontryagin-van Kampen duality theorem 5. Duality for compact and
Algebraic Number Theory
I: Algebraic Integers.- II: The Theory of Valuations.- III: Riemann-Roch Theory.- IV: Abstract Class Field Theory.- V: Local Class Field Theory.- VI: Global Class Field Theory.- VII: Zeta Functions
Abelian Groups
Infinite Abelian GroupsBy Laszlo Fuchs. Vol. 1. (Pure and Applied Mathematics, Vol. 36.) Pp. xi + 290. (Academic Press: New York and London, January 1970.) 140s.