2-Groupe des classes positives dʹun corps de nombres et noyau sauvage de la K-théorie

We compute the 2-rank of the wild kernel WK2(F) of a number field by constructing a 2-class group ad hoc. The main result generalizes in the more intricate case the canonical isomorphism established for odd primes under the assumption in a previous article (cf. (Acta. Arith. 67 (1994) 335; Math. Z. 238 (2001) 335)). It involves a criterium of triviality for the 2-part of the wild kernel of Galois number fields and, in the particular case of quadratic fields, it leads to a logarithmic interpretation of the diophantine conditions obtained by other authors.