Construction of p-adic semi-stable representations

The aim of this work is to generalize to the semi-stable setting the Fonraine-Laffaille crystalline theory. Let k be a perfect field of caracteristic p > 0, W the Witt vectors in k, K-0 = Fr(W) and S = W<u> the p-adic completion of the P.D. polynomial algebra. We define a category of S-modules with p-torsion and show it is abelian and has the same simple objects as Fontaine-Laffaille's <(MF)under bar>(f.p-2)(tvr) category. We define an exact and fully faithfull functor from this category to the category of p-adic representations of Gal((K) over bar(0)/K-0) of finite length. We define "strongly divisible" free S-modules and show how one can build p-adic semi-stable representations with them, using the previous torsion theory. By finding strongly divisible S-modules in dimension 2, we build all the dimension 2 p-adic semi-stable representations with differences in Hodge-Tate weights not exceeding p - 2. (C) Elsevier, Paris.