Ramification groups and Artin conductors of radical extensions of
Journal de théorie des nombres de Bordeaux, Volume 16 (2004) no. 3, pp. 779-816.

We study the ramification properties of the extensions (ζ m ,a m)/ under the hypothesis that m is odd and if pm than either pv p (a) or p v p (m) v p (a) (v p (a) and v p (m) are the exponents with which p divides a and m). In particular we determine the higher ramification groups of the completed extensions and the Artin conductors of the characters of their Galois group. As an application, we give formulas for the p-adique valuation of the discriminant of the studied global extensions with m=p r .

Nous étudions les propriétés de ramification des extensions (ζ m ,a m)/ sous l’hypothèse que m est impair et si pm, ou bien pv p (a) ou bien p v p (m) v p (a) (v p (m) et v p (a) sont les exposants avec lesquels p divise a et m). En particulier, nous déterminons les groupes de ramification supérieurs des extensions complétées et les conducteurs d’Artin des caractères de leur groupe de Galois. A titre d’application, nous donnons des formules pour la valuation p-adique du discriminant des extensions globales considérées avec m=p r .

DOI: 10.5802/jtnb.470
Filippo Viviani 1

1 Universita’ degli studi di Roma Tor Vergata Dipartimento dimatematica via della ricerca scientifica 1 00133 Roma, Italy
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Filippo Viviani. Ramification groups and Artin conductors of radical extensions of $\mathbb{Q}$. Journal de théorie des nombres de Bordeaux, Volume 16 (2004) no. 3, pp. 779-816. doi : 10.5802/jtnb.470. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.470/

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