[en] We develop Kummer theory for algebraic function fields in finitely many transcendental variables. We consider any finitely generated Kummer extension (possibly, over a cyclotomic extension) of an algebraic function field, and describe the structure of its Galois group. Our results show in a precise sense how the questions of computing the degrees of these extensions and of computing the group structures of their Galois groups reduce to the corresponding questions for the Kummer extensions of their constant fields.
Disciplines :
Mathématiques
Auteur, co-auteur :
BARIL BOUDREAU, Félix ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
PERUCCA, Antonella ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Co-auteurs externes :
no
Langue du document :
Anglais
Titre :
Kummer theory for function fields
Date de publication/diffusion :
2025
Titre du périodique :
Journal of Number Theory
ISSN :
0022-314X
eISSN :
1096-1658
Maison d'édition :
Elsevier, Atlanta, Géorgie
Peer reviewed :
Peer reviewed vérifié par ORBi
Focus Area :
Physics and Materials Science
Projet FnR :
FNR17921905 - Studies In The Explicit And The Statistical Aspects Of Modular Forms And Elliptic Curves, 2023 (01/04/2024-31/03/2026) - Gabor Wiese
Intitulé du projet de recherche :
Studies In The Explicit And The Statistical Aspects Of Modular Forms And Elliptic Curves
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