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
Familles d’extensions de corps de nombres -rationnels
Dans cet article, nous déterminons et classifions toutes les extensions cycliques de degré de corps de nombres -rationnels contenant une racine primitive -ième de l’unité. (Cette notion est plus générale que celle de -régularité étudiée dans un travail antérieur).
Formulae for the relative class number of an imaginary abelian field in the form of a product of determinants
Frobenius groups and integral bases.
Führer, Diskriminante und Verzweigungskörper relativ-Abelscher Zahlkörper.
Galois generators and the subspace theorem.
Gaussian primes
Generalized Kummer theory and its applications
In this report we study the arithmetic of Rikuna’s generic polynomial for the cyclic group of order and obtain a generalized Kummer theory. It is useful under the condition that and where is a primitive -th root of unity and . In particular, this result with implies the classical Kummer theory. We also present a method for calculating not only the conductor but also the Artin symbols of the cyclic extension which is defined by the Rikuna polynomial.
Good reduction of elliptic curves in abelian extensions.
Hasse-Witt matrices and Kummer extension
A simple calculation of the Hasse-Witt matrix is used to give examples of curves which are Kummer coverings of the projective line and which have easily determined p-rank. A family of curve carrying non-classical vector bundles of rank 2 is also given.
Higher degree Harrison equivalence and Milnor -functor
Ideal class groups of cubic cyclic fields