Class fields, Dirichlet characters and extended genus fields of global function fields
Number Theory
2022-04-06 v3
Abstract
We obtain the extended genus field of an abelian extension of a rational function field. We follow the definition of Angl\`es and Jaulent, which uses class field theory. First we show that the natural definition of extended genus field of a cyclotomic function field obtained by means of Dirichlet characters is the same as the one given by Angl\`es and Jaulent. Next we study the extended genus field of a finite abelian extension of a rational function field along the lines of the study of genus fields of abelian extensions of rational function fields and compare this approach with the one given by Angl\`es and Jaulent.
Keywords
Cite
@article{arxiv.2108.08337,
title = {Class fields, Dirichlet characters and extended genus fields of global function fields},
author = {Martha Rzedowski-Calderón and Gabriel Villa-Salvador},
journal= {arXiv preprint arXiv:2108.08337},
year = {2022}
}
Comments
16 pages. arXiv admin note: text overlap with arXiv:1901.07156