The Hasse conjecture for cyclic extensions.
The imaginary cyclic sextic fields with class numbers equal to their genus class numbers
It is known that there are only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Here, we determine all the imaginary cyclic sextic fields with class numbers equal to their genus class numbers.
The narrow class groups of some ℤₚ-extensions over the rationals
The ring of integers of an abelian number field.
Tours de Hilbert des extensions cubiques cycliques de Q.
Trivialité du -rang du noyau hilbertien
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...
Über die Idealklassengruppe des Dirichletschen biquadratischen Zahlenkörpers
Über die Theorie der Relativ-Abel'schen-cubischen Zahlkörper [Book]
Über relativ-invariante Kreiseinheiten und Stickelberger-Elemente.
Ueber das Fundamentalsystem und die Discriminante der Gattungen algebraischer Zahlen, welche aus Wurzelgrössen gebildet sind.
Ueber die Theorie der relativ- Abel´schen Zahlkörper
Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields
We investigate as Galois module the unit group of biquadratic extensions of number fields. The -rank of the first cohomology group of units of is computed for general . For imaginary quadratic we determine a large portion of the cases (including all unramified ) where the index takes its maximum value , where are units mod torsion of and are units mod torsion of one of the 3 quadratic subfields of .
Unités d’une famille de corps liés à la courbe
On étudie une famille de corps réels cycliques de degré 10 liés à la courbe modulaire . Les unités modulaires déterminent un sous-groupe d’unités d’indice fini. Sous certaines conditions, cet indice est égal à 1 ou 5.
Units in real Abelian fields
Untersuchungen über relativ Abelsche Zahlkörper.
When is the order generated by a cubic, quartic or quintic algebraic unit Galois invariant: three conjectures
Let be an algebraic unit of the degree . Assume that the extension is Galois. We would like to determine when the order of is -invariant, i.e. when the complex conjugates of are in , which amounts to asking that , i.e., that these two orders of have the same discriminant. This problem has been solved only for by using an explicit formula for the discriminant of the order . However, there is no known similar formula for . In the present paper, we put forward and motivate three...
Z l -extensions, fonctions L l-adiques et unités cyclotomiques.
Zur Arithmetik der zyklischen p-Körper.
Zur Arithmetik in abelschen Zahlkörpern.
Zur Theorie der n-ten Potenzreste in algebraischen Zahlkörpern. II. Über n-te Normenreste.