Genus fields of abelian extensions of congruence rational function fields
Number Theory
2014-08-19 v2
Abstract
In the published version of this paper [Finite Fields and Their Applications {\bf 20} (2013) 40--54], there is an error in the proof of Theorem 4.2 of the paper. Here we correct the error and give the right statments for Theorems 4.2, 4.5 and 5.2 We give a construction of genus fields for congruence function fields. First we consider the cyclotomic function field case following the ideas of Leopoldt and then the general case. As applications we give explicitly the genus fields of Kummer, Artin--Schreier and cyclic --extensions. Kummer extensions were obtained previously by G. Peng and Artin--Schreier extensions were obtained by S. Hu and Y. Li.
Keywords
Cite
@article{arxiv.1206.4946,
title = {Genus fields of abelian extensions of congruence rational function fields},
author = {Myriam Maldonado-Ramírez and Martha Rzedowski-Calderón and Gabriel Villa-Salvador},
journal= {arXiv preprint arXiv:1206.4946},
year = {2014}
}
Comments
15 pages