Rocky Mountain Journal of Mathematics

Genus fields of abelian extensions of rational congruence function fields, II

Jonny Fernando Barreto-Castaneda, Carlos Montelongo-Vazquez, Carlos Daniel Reyes-Morales, Martha Rzedowski-Calderon, and Gabriel Villa-Salvador

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In this paper, we find the genus field of finite abelian extensions of the global rational function field. We introduce the term conductor of constants for these extensions and determine it in terms of other invariants. We study the particular case of finite abelian $p$-extensions and give an explicit description of their genus field.

Article information

Rocky Mountain J. Math., Volume 48, Number 7 (2018), 2099-2133.

First available in Project Euclid: 14 December 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11R58: Arithmetic theory of algebraic function fields [See also 14-XX]
Secondary: 11R29: Class numbers, class groups, discriminants 11R60: Cyclotomic function fields (class groups, Bernoulli objects, etc.)

Global function fields ramification genus fields abelian $p$-extensions


Barreto-Castaneda, Jonny Fernando; Montelongo-Vazquez, Carlos; Reyes-Morales, Carlos Daniel; Rzedowski-Calderon, Martha; Villa-Salvador, Gabriel. Genus fields of abelian extensions of rational congruence function fields, II. Rocky Mountain J. Math. 48 (2018), no. 7, 2099--2133. doi:10.1216/RMJ-2018-48-7-2099.

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