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math.NT2024
Extended genus fields of abelian extensions of rational function fields
Juan Carlos Hernandez-Bocanegra, Gabriel Villa-Salvador
In this paper we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power deg…
math.NT2024
A note on extended genus fields of Kummer extensions of rational function fields
Martha Rzedowski-Calderón, Gabriel Villa-Salvador
We consider the generalization of the extended genus field of a prime degree cyclic Kummer extension of a rational function field obtained by R. Clement in 1992 to general Kummer e…