Representations semi-stables de torsion dans le cas peu ramifie

Abstract

Let K be a local field of mixed characteristic not absolutely ramified. Fontaine-Laffaille theory 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 thoery for the semi-stable representations. 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.