Torsion representations arising from $(\phi ,\hat{G})$-modules

Abstract

The notion of a $(\phi ,\hat{G})$-module is defined by Tong Liu in 2010 to classify lattices in semi-stable representations. In this paper, we study torsion $(\phi ,\hat{G})$-modules, and torsion p-adic representations associated with them, including the case where p=2. First we prove that the category of torsion p-adic representations arising from torsion $(\phi ,\hat{G})$-modules is an abelian category. Secondly, we construct a maximal (minimal) theory for $(\phi ,\hat{G})$-modules by using the theory of étale $(\phi ,\hat{G})$-modules, essentially proved by Xavier Caruso, which is an analogue of Fontaine's theory of étale $(\phi ,\Gamma )$-modules. Non-isomorphic two maximal (minimal) objects give non-isomorphic two torsion p-adic representations.

arXiv admin note: significant text overlap with arXiv:1105.5477