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General concepts and strategies are developed for identifying the isomorphism type of the second -class group , that is the Galois group of the second Hilbert -class field , of a number field , for a prime . The isomorphism type determines the position of on one of the coclass graphs , , in the sense of Eick, Leedham-Green, and Newman. It is shown that, for special types of the base field and of its -class group , the position of is restricted to certain admissible branches of coclass...
The so-called Lifted Root Number Conjecture is a strengthening of Chinburg’s -
conjecture for Galois extensions of number fields. It is certainly more difficult
than the -localization. Following the lead of Ritter and Weiss, we prove the Lifted Root Number
Conjecture for the case that and the degree of is an odd prime, with
another small restriction on ramification. The very explicit calculations with cyclotomic
units use trees and some classical combinatorics for bookkeeping. An important...
Soit un corps de nombres contenant et muni d’un groupe d’automorphismes d’ordre étranger à ; pour toute représentation -irréductible de , de caractère , et tout -module , soit rg l’entier maximum tel que contienne . Nous établissons par exemple la formule générale explicite suivante :où et sont des ensembles finis disjoints de places de tels que contienne les places au-dessus de , où est le groupe de classes généralisées qui correspond, par le corps de classes, au...
Nous établissons les résultats fondamentaux de la théorie -adique globale du corps de classes pour les corps de nombres.
We give exhaustive list of biquadratic fields and without -exotic symbol, i.e. for which the -rank of the Hilbert kernel (or wild kernel) is zero. Such are logarithmic principals [J3]. We detail an exemple of this technical numerical exploration and quote the family of theories and results we utilize. The -rank of tame, regular and wild kernel of -theory are connected with local and global problem of embedding in a -extension. Global class field theory can describe the -rank of the Hilbert...
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