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Capitulation for even K -groups in the cyclotomic ℤ p -extension.

Romain Validire (2009)

Journal de Théorie des Nombres de Bordeaux

Let p be a prime number and F be a number field. Since Iwasawa’s works, the behaviour of the p -part of the ideal class group in the ℤ p -extensions of F has been well understood. Moreover, M. Grandet and J.-F. Jaulent gave a precise result about its abelian p -group structure.On the other hand, the ideal class group of a number field may be identified with the torsion part of the K 0 of its ring of integers. The even K -groups of rings of integers appear as higher versions of the class group. Many authors...

Classes logarithmiques signées des corps de nombres

Jean-François Jaulent (2000)

Journal de théorie des nombres de Bordeaux

Nous définissons le 2 -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.

Computation of 2-groups of positive classes of exceptional number fields

Jean-François Jaulent, Sebastian Pauli, Michael E. Pohst, Florence Soriano–Gafiuk (2008)

Journal de Théorie des Nombres de Bordeaux

We present an algorithm for computing the 2-group 𝒞 ℓ F p o s of the positive divisor classes in case the number field F has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel W K 2 ( F ) in K 2 ( F ) .

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