Genus fields of Kummer extensions of rational function fields
Number Theory
2021-05-17 v1
Abstract
In this paper we obtain the genus field of a general Kummer extension of a global rational function field. We study first the case of a general Kummer extension of degree a power of a prime. Then we prove 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. Our main result, the genus of a general Kummer extension of a global rational function field, is a direct consequence of this fact.
Keywords
Cite
@article{arxiv.2105.06627,
title = {Genus fields of Kummer extensions of rational function fields},
author = {Martha Rzedowski-Calderón and Gabriel Villa-Salvador},
journal= {arXiv preprint arXiv:2105.06627},
year = {2021}
}
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16 pages