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math.NT2021
Class fields, Dirichlet characters and extended genus fields of global function fields
Martha Rzedowski-Calderón, Gabriel Villa-Salvador
We obtain the extended genus field of an abelian extension of a rational function field. We follow the definition of Anglès and Jaulent, which uses class field theory. First we sho…
math.NT2021
Genus fields of Kummer extensions of rational function fields
Martha Rzedowski-Calderón, Gabriel Villa-Salvador
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 o…