2021/05/14 by Rzedowski-Calderón, Martha, Villa-Salvador, Gabriel
#11R60 #FOS: Mathematics #Number Theory (math.NT) #Primary 11R58 #Secondary 11R29
paper · doi:10.48550/arxiv.2105.06627
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.