\(\ell\)-class groups of cyclic function fields of degree \(\ell\)

DOI10.1016/J.FFA.2005.09.001zbMath1176.11061OpenAlexW2010308979MaRDI QIDQ946886

Christian Wittmann

Publication date: 25 September 2008

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2005.09.001

zbMATH Keywords

function fieldsPicard groupideal class groupcyclic extensions

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Cyclotomic function fields (class groups, Bernoulli objects, etc.) (11R60) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33)

Related Items (12)

Densities for 4-class ranks of quadratic function fields ⋮ The generalized Rédei-matrix for function fields ⋮ Capitulation problem for global function fields ⋮ Genus fields of abelian extensions of rational congruence function fields. II ⋮ Density of class groups of imaginary \(\ell \)-cyclic function fields ⋮ 3-Class groups of cubic cyclic function fields ⋮ The genus fields of Artin-Schreier extensions ⋮ Indivisibility of divisor class numbers of Kummer extensions over the rational function field ⋮ Infinite families of cyclotomic function fields with any prescribed class group rank ⋮ Genus fields of congruence function fields ⋮ GENUS FIELDS OF CYCLIC l-EXTENSIONS OF RATIONAL FUNCTION FIELDS ⋮ Function field genus theory for non-Kummer extensions

Cites Work

• Ambiguous divisor classes in function fields
• Genus theory of global fields
• The 2-primary class group of certain hyperelliptic curves
• The genus fields of Kummer function fields.
• Two-torsion of the Jacobian of hyperelliptic curves over finite fields
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