[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)
Language :
English
Title :
Kummer theory for function fields
Publication date :
n.d.
Number of pages :
15
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
