Calcul de groupes de classes
Calcul de nombres de classes par dévissage des unités cyclotomiques
Capitulation for even -groups in the cyclotomic -extension.
Let be a prime number and be a number field. Since Iwasawa’s works, the behaviour of the -part of the ideal class group in the -extensions of has been well understood. Moreover, M. Grandet and J.-F. Jaulent gave a precise result about its abelian -group structure.On the other hand, the ideal class group of a number field may be identified with the torsion part of the of its ring of integers. The even -groups of rings of integers appear as higher versions of the class group. Many authors...
Class fields of abelian extensions of Q.
Class group of a cyclotomic -extension
Class Group Rank Relations in Zl-Extensions.
Class groups of abelian fields, and the main conjecture
This first part of this paper gives a proof of the main conjecture of Iwasawa theory for abelian base fields, including the case , by Kolyvagin’s method of Euler systems. On the way, one obtains a general result on local units modulo circular units. This is then used to deduce theorems on the order of -parts of -class groups of abelian number fields: first for relative class groups of real fields (again including the case ). As a consequence, a generalization of the Gras conjecture is stated...
Class number calculation of a cubic field from the elliptic unit.
Class number calculation of a quartic field from the elliptic unit
Class number calculation of a sextic field from the elliptic unit
Class number formulae for imaginary quadratic fields.
Class number formulae for imaginary quadratic fields. II.
Class number relations in pure sextic fields.
Class numbers and periodic smooth maps.
Class Numbers and Zp-Extensions.
Class Numbers in Zd-p-Extensions.
Class Numbers in Zdp-extensions-II.
Class Numbers in Z....-Extensions. III.
Class Numbers in Z...-extensions. IV.
Class numbers of binary quadratic forms over algebraic number fields.