2-extensions of ℚ with trivial 2-primary Hilbert kernel
A bound for the torsion in the -theory of algebraic integers.
A new algorithm for the computation of logarithmic -class groups of number fields.
A reciprocity law for K2-traces.
A twisted class number formula and Gross's special units over an imaginary quadratic field
Let be a finite abelian extension of number fields with imaginary quadratic. Let be the ring of integers of and a rational integer. We construct a submodule in the higher odd-degree algebraic -groups of using corresponding Gross’s special elements. We show that this submodule is of finite index and prove that this index can be computed using the higher “twisted” class number of , which is the cardinal of the finite algebraic -group .
An idelic approach to the wild kernel.
Analogues étales de la -tour des corps de classes
Nous construisons un analogue «tordu» de la -tour de corps de classes d’un corps de nombres ( un nombre premier) et étudions ses liens avec la théorie d’Iwasawa. Le résultat principal donne un critère du type Golod et Shafarevich pour que la tour «tordue» soit infinie.
Analogues supérieurs du noyau sauvage
Bounds For Étale Capitulation Kernels II
Let be an odd prime and a cyclic -extension of number fields. We give a lower bound for the order of the kernel and cokernel of the natural extension map between the even étale -groups of the ring of -integers of , where is a finite set of primes containing those which are -adic.
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 groups and general linear group cohomology for a ring of algebraic integers.
Classes logarithmiques ambiges des corps quadratiques
Classes logarithmiques au sens restreint.
Classes logarithmiques signées des corps de nombres
Nous définissons le -groupe des classes logarithmiques signées d’un corps de nombres par analogie avec le groupe des classes d’idéaux au sens restreint et nous établissons les résultats de base de l’arithmétique des classes logarithmiques signées.
Codescente en K-théorie étale et corps de nombres.
Computation of 2-groups of positive classes of exceptional number fields
We present an algorithm for computing the 2-group of the positive divisor classes in case the number field has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel in .
Conditions under which is not generated by Dennis-Stein symbols
Corrigendum à «Classes logarithmiques signées des corps de nombres»
Nous corrigeons une erreur contenue dans un article précédent où sont données deux définitions prétendument équivalentes du -groupe des classes logarithmiques signées d’un corps de nombres.
Corrigendum to the paper "On the 2-primary part of a conjecture of Birch and Tate" (Acta Arith. 43 (1983), 69-81)
Densities of 4-ranks of K₂(𝒪)