Kummer theory for products of one-dimensional tori

English

Perissinotto, Flavio[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) >]

Undated

No

[en] Kummer theory ; Tori ; Field Extensions

[en] Let T be a finite product of one-dimensional tori defined over a number field K. We consider the torsion-Kummer extension K(T[nt], (1/n)G), where n,t are positive integers and G is a finitely generated group of K-points on T. We show how to compute the degree of K(T[nt], (1/n)G) over K and how to determine whether T is split over such an extension. If K=Q, then we may compute at once the degree of the above extensions for all n and t.