Genus fields of finite abelian extensions

Jonny Fernando Barreto-Castañeda, Carlos Montelongo-Vázquez, Carlos Daniel Reyes-Morales, Martha Rzedowski-Calderón, Gabriel Villa-Salvador

Published 2017-09-20Version 1

In this paper we find the genus field of a finite abelian extension of the global rational function field. We introduce the term conductor of constants for these extensions and determine it in terms of other invariants. We study the particular case of finite abelian $p$- extensions. Finally, we give an explicit description of the genus field of any finite abelian $p$--extension of a global rational function field.