SÉMINAIRE DE THÉORIE DES NOMBRES 2000-2001
Le Vendredi à 15 heures 30 en Salle de Conférence
Organisateur : Arnaud Jehanne
Université de Saint-PetersbourgOn Milnor's K-groups of higher local fields
We discuss the structure of the nth Milnor K-group of an n-dimensional local field modulo its maximal divisible subgroup. This group plays a fundamental role in the higher local class field theory developed by Parshin, Kato and Fesenko. The structure of this group in the mixed characteristic case is not completely known. We prove that the wild part of this group is topologically generated, up to a finitely generated quotient, by torsion elements. We can give a complete description of the group under consideraion in the absolutely unramified case.