Genus fields of abelian extensions of rational congruence function fields

Myriam Maldonado-Ramírez; Martha Rzedowski-Calderón; Gabriel Villa-Salvador

doi:10.1016/j.ffa.2012.09.006

Genus fields of abelian extensions of rational congruence function fields

Myriam Maldonado-Ramírez, Martha Rzedowski-Calderón, Gabriel Villa-Salvador

Escuela Superior de Física y Matemáticas (ESFM)

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	40-54
Number of pages	15
Journal	Finite Fields and their Applications
Volume	20
Issue number	1
DOIs	https://doi.org/10.1016/j.ffa.2012.09.006
State	Published - Mar 2013

Keywords

Artin-Schreier extensions
Congruence function fields
Cyclotomic function fields
Dirichlet characters
Genus fields
Global fields
Kummer extensions
Witt vectors

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10.1016/j.ffa.2012.09.006

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title = "Genus fields of abelian extensions of rational congruence function fields",

abstract = "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.",

keywords = "Artin-Schreier extensions, Congruence function fields, Cyclotomic function fields, Dirichlet characters, Genus fields, Global fields, Kummer extensions, Witt vectors",

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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 -

Genus fields of abelian extensions of rational congruence function fields

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Keywords

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