Ramification groups and Artin conductors of radical extensions of the rationals

Details Ramification groups and Artin conductors of radical extensions of the rationals Ramification groups and Artin conductors of radical extensions of the rationals

2004-09-27

arxiv.org/abs/math/0409533v1

Journal des Theorie des Nombres de Bordeaux 16 (2004), 779-816

Mathematics

Number Theory

29 pages, to be published on the Journal de Theorie de Nombres de Bourdeaux

Scientific paper

We compute the higher ramification groups and the Artin conductors of radical extensions of the rationals. As an application, we give formulas for their discriminant (using the conductor-discriminant formula). The interest in such number fields is due to the fact that they are among the simplest non-abelian extensions of the rationals (and so not classified by Class Field Theory). We show that this extensions have non integer jumps in the superior ramification groups, contrarily to the case of abelian extensions (as prescribed by Hasse-Arf theorem).

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