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arXiv · 2208.08393

Genus Field and Extended Genus Field of an Elementary Abelian Extension of Global Fields

Juan Carlos Hernandez-Bocanegra·Gabriel Villa-Salvador
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Abstract

In the present work we give the construction of the genus field and the extended genus field of an elementary abelian $l$-extension of a field of rational functions, where $l$ is a prime number. In the Kummer case, if $K$ is contained in a cyclotomic funtion field, the construction is given using Leopoldt's ideas by means of Dirichlet characters. Following the definition of Angl\`es and Jaulent of extended Hilbert class field, we obtain the extended genus field of an elementary abelian $l$-extension of a field of rational functions.

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Juan Carlos Hernandez-Bocanegra, Gabriel Villa-Salvador. 2022-08-17. Genus Field and Extended Genus Field of an Elementary Abelian Extension of Global Fields. https://arxiv.org/abs/2208.08393

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