Abstract
Let K be a local field of mixed characteristic not absolutely ramified. Fontaine-Laaille theory (see [J. M. Fontaine et G. Laffaille, Construction de représentations p-adiques, Ann. Sci. ENS 15 (1982), 547–608. ]) gives a description of the torsion crystalline ℤp 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 [C. Breuil, Construction de représentations p-adiques semi-stables, Ann. Sci. ENS 31 (1997), 281–327]).
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.
© Walter de Gruyter
