Function field genus theory for non-Kummer extensions
Number Theory
2022-04-06 v1
Abstract
In this paper we first obtain the genus field of a finite abelian non-Kummer --extension of a global rational function field. Then, using that the genus field of a composite of two abelian extensions of a global rational function field with relatively prime degrees is equal to the composite of their respective genus fields and our previous results, we deduce the general expression of the genus field of a finite abelian extension of a global rational function field.
Keywords
Cite
@article{arxiv.2204.01874,
title = {Function field genus theory for non-Kummer extensions},
author = {Martha Rzedowski-Calderón and Gabriel Villa-Salvador},
journal= {arXiv preprint arXiv:2204.01874},
year = {2022}
}
Comments
11 pages