We study the ramification properties of the extensions Q(03B6m, m~03B1)/Q under the hypothesis that m is odd and if p| m than either p vp (a) or pvp(m)| vp(03B1) (vp(03B1) and vp(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 =Pr.
Viviani, F. (2004). Ramification groups and Artin conductors of radical extensions of the rationals. JOURNAL DE THÉORIE DES NOMBRES DE BORDEAUX, 16(3), 779-816 [10.5802/jtnb.470].
Ramification groups and Artin conductors of radical extensions of the rationals
Viviani F.
2004-01-01
Abstract
We study the ramification properties of the extensions Q(03B6m, m~03B1)/Q under the hypothesis that m is odd and if p| m than either p vp (a) or pvp(m)| vp(03B1) (vp(03B1) and vp(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 =Pr.| File | Dimensione | Formato | |
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