2-Groupe des classes positives d'un corps de nombres et noyau sauvage de la K-théorie

✍ Scribed by Jean-Francois Jaulent; Florence Soriano-Gafiuk

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 340 KB
• Volume: 108
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2003.09.012

✦ Synopsis

We compute the 2-rank of the wild kernel WK 2 ðF Þ of a number field by constructing a 2class group ad hoc. The main result generalizes in the more intricate case l ¼ 2 the canonical isomorphism l m F # Z f Cl Cl F C l WK 2 ðF Þ established for odd primes l under the assumption m l CF 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.