Normes cyclotomiques na{ï}ves et unit{é}s logarithmiques

Abstract

We compute the Z-rank of the subgroup of elements of the multiplicative group of a number field K that are norms from every finite level of the cyclotomic Z{\ell}-extension of K. Thus we compare its {\ell}-adification with the group of logarithmic units of K. By the way we point out an easy proof of the Gross-Kuz'min conjecture for {\ell}-undecomposed extensions of abelian fields.

in French