Zobrazeno 1 - 10
of 116
pro vyhledávání: '"Villa–Salvador, Gabriel"'
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
Externí odkaz:
http://arxiv.org/abs/2404.17566
We consider the generalization of the extended genus field of a prime degree cyclic Kummer extension of a rational function field obtained by R. Clement in 1992 to general Kummer extensions. We observe that the same approach of Clement works in gener
Externí odkaz:
http://arxiv.org/abs/2403.01021
Autor:
Rzedowski-Calderón, Martha1 (AUTHOR), Villa-Salvador, Gabriel1 (AUTHOR) gvillasalvador@gmail.com
Publikováno v:
Axioms (2075-1680). Nov2024, Vol. 13 Issue 11, p734. 8p.
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
Externí odkaz:
http://arxiv.org/abs/2208.08393
In this paper we first obtain the genus field of a finite abelian non-Kummer $l$--extension of a global rational function field. Then, using that the genus field of a composite of two abelian extensions of a global rational function field with relati
Externí odkaz:
http://arxiv.org/abs/2204.01874
We obtain the extended genus field of an abelian extension of a rational function field. We follow the definition of Angl\`es and Jaulent, which uses class field theory. First we show that the natural definition of extended genus field of a cyclotomi
Externí odkaz:
http://arxiv.org/abs/2108.08337
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 ab
Externí odkaz:
http://arxiv.org/abs/2105.06627
We give a construction of the genus field for Kummer $\ell^n$-cyclic extensions of rational congruence function fields, where $\ell$ is a prime number. First, we compute the genus field of a field contained in a cyclotomic function field, and then fo
Externí odkaz:
http://arxiv.org/abs/2006.11870
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
Externí odkaz:
http://arxiv.org/abs/1901.07156
Publikováno v:
In Finite Fields and Their Applications January 2023 85