Genus fields of Kummer extensions of rational function fields

Autor:	Rzedowski-Calderón, Martha, Villa-Salvador, Gabriel
Rok vydání:	2021
Předmět:	Mathematics - Number Theory Primary 11R58 Secondary 11R29 11R60
Druh dokumentu:	Working Paper
Popis:	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. Comment: 16 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2105.06627 Zobrazit plný text záznamu View this record from Arxiv