(phi, Gamma)-modules et loi explicite de réciprocité

Abstract : The framework of this thesis is the theory of p-adic representations, in particular Fontaine's theory. I am interested in the case of a metabelian extension of a local field, I build a (phi, Gamma)-module adapted to this extension, then generalizations of some usual tools associated with this (phi, Gamma)-module are given, such as a complex calculating the cohomology of the representation. Furthermore, I establish explicit formulas of the dictionnary between the word of representations and the one of (phi, Gamma)-modules, for the Herr complex, the cup-product or Kummer's map.

The second part of this work is devoted to the proof of Brückner-Vostokov reciprocity law for a formal group. Combining methods of (phi, Gamma)-modules and specified techniques introduced by Abrashkin with a cohomological interpretation of his work, I give a proof of the reciprocity law free from the non natural assumption that roots of unity belong to the base field.
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Mathématiques [math]. Université de Franche-Comté, 2008. Français
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Floric Tavares Ribeiro. (phi, Gamma)-modules et loi explicite de réciprocité. Mathématiques [math]. Université de Franche-Comté, 2008. Français. 〈tel-00379771〉



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