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arXiv · 2105.06627

Genus fields of Kummer extensions of rational function fields

Martha Rzedowski-Calderón·Gabriel Villa-Salvador
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Abstract

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 of a prime. Then we prove that the genus field of a composite of two abelian extensions of a global rational function field with relatively prime degrees is equal to the composite of their respective genus fields. Our main result, the genus of a general Kummer extension of a global rational function field, is a direct consequence of this fact.

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Martha Rzedowski-Calderón, Gabriel Villa-Salvador. 2021-05-14. Genus fields of Kummer extensions of rational function fields. https://arxiv.org/abs/2105.06627

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