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arXiv · 1709.06697

Genus fields of finite abelian extensions

Jonny Fernando Barreto-Castañeda·Carlos Montelongo-Vázquez·Carlos Daniel Reyes-Morales·Martha Rzedowski-Calderón·Gabriel Villa-Salvador
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Abstract

In this paper we find the genus field of finite abelian extensions of the global rational function field. We introduce the term conductor of constants for these extensions and determine it in terms of other invariants. We study the particular case of finite abelian $p$--extensions and give an explicit description of their genus field.

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Jonny Fernando Barreto-Castañeda, Carlos Montelongo-Vázquez, Carlos Daniel Reyes-Morales, Martha Rzedowski-Calderón, Gabriel Villa-Salvador. 2017-10-21. Genus fields of finite abelian extensions. https://arxiv.org/abs/1709.06697

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