2-Groupe des classes positives d'un corps de nombres et noyau sauvage de la K-théorie |
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Authors: | Jean-Francois Jaulent Florence Soriano-Gafiuk |
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Affiliation: | a Université Bordeaux 1, Institut de Mathématiques 351, cours de la Libération, TALENCE Cedex F-33405, France b Université de Metz, Département de Mathématiques, Ile du Saulcy, METZ Cedex F-57045, France |
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Abstract: | 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. |
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Keywords: | Wild kernel k-theory Logarithmic classes Positive classes |
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