Genus fields of global fields

Elizabeth Ramírez-Ramírez; Martha Rzedowski-Calderón; Gabriel Villa-Salvador

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arXiv · 1901.07156

Genus fields of global fields

Elizabeth Ramírez-Ramírez·Martha Rzedowski-Calderón·Gabriel Villa-Salvador

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Abstract

In this paper we obtain the extended genus field of a global field. First we define the extended genus field of a global function field and we obtain, via class field theory, the description of the extended genus field of an arbitrary global function field. In the last part of the paper we use the techniques for function fields to describe the extended genus field of an arbitrary number field.

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Elizabeth Ramírez-Ramírez, Martha Rzedowski-Calderón, Gabriel Villa-Salvador. 2019-01-22. Genus fields of global fields. https://arxiv.org/abs/1901.07156

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