TY - JOUR
T1 - Genus fields of abelian extensions of rational congruence function fields
AU - Maldonado-Ramírez, Myriam
AU - Rzedowski-Calderón, Martha
AU - Villa-Salvador, Gabriel
PY - 2013/3
Y1 - 2013/3
N2 - 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 p-extensions. Kummer extensions were obtained previously by G. Peng and Artin-Schreier extensions were obtained by S. Hu and Y. Li.
AB - 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 p-extensions. Kummer extensions were obtained previously by G. Peng and Artin-Schreier extensions were obtained by S. Hu and Y. Li.
KW - Artin-Schreier extensions
KW - Congruence function fields
KW - Cyclotomic function fields
KW - Dirichlet characters
KW - Genus fields
KW - Global fields
KW - Kummer extensions
KW - Witt vectors
UR - http://www.scopus.com/inward/record.url?scp=84873164112&partnerID=8YFLogxK
U2 - 10.1016/j.ffa.2012.09.006
DO - 10.1016/j.ffa.2012.09.006
M3 - Artículo
SN - 1071-5797
VL - 20
SP - 40
EP - 54
JO - Finite Fields and their Applications
JF - Finite Fields and their Applications
IS - 1
ER -