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Conjecture de l'inertie modérée de Serre

Abstract : The aim of this thesis is to give a complete proof of the tame inertia Serre's conjecture which gives constraints (in relation to e and r) on the Galois group of cohomology H^r_et(X_Kbar, Z/pZ) where X is a proper smooth variety with semi-stable reduction on a p-adic field K with absolute ramification index e.

In order to do that, we establish, in the case er < p-1, a period isomophism linking the former étale cohomology group and a group of log-crystalline cohomology of the special fiber of X. Then, we show that this group defines an object of the category M^r introduced by Breuil. Finally, the conclusion follows from a careful study of the objects of M^r.

The last chapter of this thesis (which is independent) is devoted to the construction of a duality on the category M^r.
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Contributor : Xavier Caruso <>
Submitted on : Wednesday, December 14, 2005 - 5:53:45 PM
Last modification on : Tuesday, October 20, 2020 - 3:56:31 PM
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  • HAL Id : tel-00011202, version 1


Xavier Caruso. Conjecture de l'inertie modérée de Serre. Mathématiques [math]. Université Paris-Nord - Paris XIII, 2005. Français. ⟨tel-00011202⟩



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