%0 Journal Article
%T Sur la pro-p-extension localement cyclotomique maximale d'un corps de nombres
%A Romain Validire
%J Mathematics
%D 2008
%I arXiv
%X Let p be a prime number and F be a number field. We consider the Galois group G over the cyclotomic Z_p extension of F of the maximal unramified, p-decomposed, pro-p-extension of the cyclotomic Z_p extension of F. The question whether G is free pro-p was already asked by many authors. In this article, we highlight a link between the freeness of G and the Galois descent for some localisation kernels. Then we give explicit criterions to show that G is not a free pro-p-group.
%U http://arxiv.org/abs/0812.1687v1