arXiv subjects

Juan Carlos Hernandez-Bocanegra

Publications and source records attributed to Juan Carlos Hernandez-Bocanegra.

2 recordsLinked to original sources

arXiv2024

Extended genus fields of abelian extensions of rational function fields

In this paper we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power degree. Next, we use that the extended genus fields of a composite of two cyclotomic extensions of a global rational function field is equal to the composite of their respective extended genus fields, to obtain our main result. This result is that the extended genus field of a general finite abelian extension of a global rational function field, is given explicitly in terms of the field and of the extended genus field of its "cyclotomic projection".

math.NT↗

arXiv2022

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

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 Anglès 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.

math.NT↗