Kummer theory for function fields

[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 :

Mathematics

Author, co-author :

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)

External co-authors :

Language :

English

Title :

Kummer theory for function fields

Publication date :

2025

Journal title :

Journal of Number Theory

ISSN :

0022-314X

eISSN :

1096-1658

Publisher :

Elsevier, Atlanta, Georgia

Peer reviewed :

Peer Reviewed verified by ORBi

Focus Area :

Physics and Materials Science

FnR Project :

FNR17921905 - Studies In The Explicit And The Statistical Aspects Of Modular Forms And Elliptic Curves, 2023 (01/04/2024-31/03/2026) - Gabor Wiese

Name of the research project :

Studies In The Explicit And The Statistical Aspects Of Modular Forms And Elliptic Curves

Available on ORBilu :

since 03 July 2024

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Bibliography

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