GENUS FIELDS OF CYCLIC l-EXTENSIONS OF RATIONAL FUNCTION FIELDS

DOI10.1142/S1793042113500243zbMath1276.11187OpenAlexW2045912401MaRDI QIDQ2840304

Victor Bautista-Ancona, Martha Rzedowski-Calderón, Gabriel Daniel Villa-Salvador

Publication date: 17 July 2013

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042113500243

zbMATH Keywords

congruence function fieldscyclotomic function fieldsKummer extensionsglobal fieldscyclic extensionsgenus fields

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Cyclotomic function fields (class groups, Bernoulli objects, etc.) (11R60) Class numbers, class groups, discriminants (11R29)

Related Items (8)

Genus fields of Kummer extensions of rational function fields ⋮ Genus field and extended genus field of an elementary abelian extension of global fields ⋮ Genus fields of abelian extensions of rational congruence function fields. II ⋮ 3-Class groups of cubic cyclic function fields ⋮ On l-class groups of global function fields ⋮ Genus fields of congruence function fields ⋮ Genus fields of Kummer ℓn-cyclic extensions ⋮ Function field genus theory for non-Kummer extensions

Cites Work

• The generalized Rédei-matrix for function fields
• Capitulation problem for global function fields
• Genus fields of congruence function fields
• \(\ell\)-class groups of cyclic function fields of degree \(\ell\)
• The genus fields of Artin-Schreier extensions
• The genus field of an algebraic function field
• Genus theory of global fields
• The genus fields of Kummer function fields.
• Central Extensions, Galois Groups, and Ideal Class Groups of Number Fields
• Zur Geschlechtertheorie in abelschen Zahlkörpern

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