A combinatorial proof of the Kronecker--Weber Theorem in positive characteristic
Number Theory
2013-07-16 v1
Abstract
In this paper we present a combinatorial proof of the Kronecker--Weber Theorem for global fields of positive characteristic. The main tools are the use of Witt vectors and their arithmetic developed by H. L. Schmid. The key result is to obtain, using counting arguments, how many --cyclic extensions exist of fixed degree and bounded conductor where only one prime ramifies are there. We then compare this number with the number of subextensions of cyclotomic function fields of the same type and verify that these two numbers are the same.
Keywords
Cite
@article{arxiv.1307.3590,
title = {A combinatorial proof of the Kronecker--Weber Theorem in positive characteristic},
author = {Julio Cesar Salas-Torres and Martha Rzedowski-Calderón and Gabriel Villa-Salvador},
journal= {arXiv preprint arXiv:1307.3590},
year = {2013}
}
Comments
17 pages