Genus theory of global fields

DOI10.1007/s002290050229zbMath0982.11062OpenAlexW1989509021MaRDI QIDQ1568834

Jean-François Jaulent, Bruno Anglès

Publication date: 27 March 2002

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002290050229

zbMATH Keywords

function fieldsclass numbernumber fieldsHilbert class fieldcurves over finite fieldsglobal fieldtotally positive elementslocal normsanalogue of sign functionsgenus theory for finite extensions of fieldsgroup of signed idealsnarrow ideal classesrestricted class group

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Class field theory (11R37) Class numbers, class groups, discriminants (11R29)

Related Items (14)

Genus fields of global fields ⋮ Genus field and extended genus field of an elementary abelian extension of global fields ⋮ Idéaux ambiges dans les corps de fonctions. (Ambiguous ideals in function fields) ⋮ Corrigendum to ``Signed logarithmic classes of number fields ⋮ Class fields, Dirichlet characters, and extended genus fields of global function fields ⋮ The generalized Rédei-matrix for function fields ⋮ Capitulation problem for global function fields ⋮ \(\ell\)-class groups of cyclic function fields of degree \(\ell\) ⋮ Genus fields of abelian extensions of rational congruence function fields. II ⋮ 3-Class groups of cubic cyclic function fields ⋮ Signed logarithmic classes of number fields ⋮ 2-group of positive classes of a number field and wild kernel of \(K\)-theory. ⋮ Genus fields of congruence function fields ⋮ GENUS FIELDS OF CYCLIC l-EXTENSIONS OF RATIONAL FUNCTION FIELDS

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