Semi-stable representations of torsion in the cas er < p-1

Let K be a local field of mixed characteristic not absolutely ramified. Fontaine-Laffaille theory (see [13]) gives a description of the torsion crystalline Z(p) representations of the absolute Galois group of K (p denotes the characteristic of the residual field). Improving the former works, Breuil introduced new modules and obtained an integer and torsion theory for the semi-stable representations (see [2]). In this paper, we follow Breuil's works and adapt them to the case where the local field K can be absolutely ramified. However, we would have a limitation on the index of absolute ramification.