Conjecture de l'inertie modérée de Serre
Xavier Caruso
Abstract
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 étale cohomology of X\Kbar with coefficients in Z/pn 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.
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