Eigenspaces of the ideal class group
The aim of this paper is to prove an analog of Gras’ conjecture for an abelian field and an odd prime dividing the degree assuming that the -part of group is cyclic.
Ein Satz über relativ-Galoissche Zahlkörper und seine Anwendang auf relativ-Abelsche Zahlkörper
Eine Aufgabe aus der algebraischen Zahlentheorie
Elliptic units of cyclic unramified extensions of complex quadratic fields
Erratum à l’article «Extensions cycliques de degré de corps de nombres -réguliers»
Etage initial d'une Zl-extension.
Existence of an unramified cyclic extension and congruence conditions
Extensions cycliques de degré sur
Extensions cycliques de degré de corps de nombres -réguliers
We determine all cyclic extensions of prime degree over a -regular number field containing the -roots of unity which are also -regular. We classify these extensions according to the ramification index of the wild place in and to the -valuation of the relative class number (which is the quotient of the ordinary class numbers of and ). We study the case where the is odd prime, since the even case was studien by R. Berger. Our genus theory methods rely essentially on G. Gras...
Extensions quadratiques 2-birationnelles de corps totalement réels.
We characterize 2-birational CM-extensions of totally real number fields in terms of tame ramification. This result completes in this case a previous work on pro-l-extensions over 2-rational number fields.
Extensions with restricted ramification and duality for arithmetic schemes