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arXiv · 2108.08337

Class fields, Dirichlet characters and extended genus fields of global function fields

Martha Rzedowski-Calderón·Gabriel Villa-Salvador
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Abstract

We obtain the extended genus field of an abelian extension of a rational function field. We follow the definition of Angl\`es and Jaulent, which uses class field theory. First we show that the natural definition of extended genus field of a cyclotomic function field obtained by means of Dirichlet characters is the same as the one given by Angl\`es and Jaulent. Next we study the extended genus field of a finite abelian extension of a rational function field along the lines of the study of genus fields of abelian extensions of rational function fields and compare this approach with the one given by Angl\`es and Jaulent.

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Martha Rzedowski-Calderón, Gabriel Villa-Salvador. 2021-08-18. Class fields, Dirichlet characters and extended genus fields of global function fields. https://arxiv.org/abs/2108.08337

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