Integral $G$-structures of Wach modules

Abstract

In this paper, we study the tannakian properties of the Fontaine-Laffaille functor ${\mathbf{V}}_{\mathbf{cris}}$ thanks to the theory of Wach's modules. We construct a point of the torsor linking cristalline representations and weakly admissible filtered modules, preserving the lattices in the sens of the Fontaine-Laffaille correspondance.