Conjecture de l'inertie modérée de Serre

Details Conjecture de l'inertie modérée de Serre Conjecture de l'inertie modérée de Serre

2005-09-29

arxiv.org/abs/math/0509685v1

Mathematics

Number Theory

57 pages

Scientific paper

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.

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