  Let K be a local field of mixte characteristics. We assume that the residue
field is perfect. Let X\_K be a proper smooth scheme over K admitting an
integer model X which is proper and semi-stable. In this article, we prove a
period isomorphism linking the \'{e}tale cohomology of X\_Kbar with
coefficients in Z/p^n and the log-crystalline cohomology of the special fiber
of X. Nevertheless, we have a restriction on the absolute ramification of K and
the degree of the cohomologies. We apply the theory to deduce a complete proof
of the Serre conjecture on the tame inertia.
