Abstract

In this thesis we focus our research on constructing two new types of Fontaine sheaves, [Special characters omitted.] and A max in the third chapter and the fourth one respectively and in proving some of their main properties, most important the localization over small affines. This pair of new sheaves plays a crucial role in generalizing a comparison isomorphism theorem of Faltings for the ramified case. In the first chapter we introduce the concept of p -adic Galois representation and provide and analyze some examples. The second chapter is an overview of the Fontaine Theory. We define the concept of semi-linear representation and study the period rings introduced by Fontaine while understanding their importance in classifying the p -adic Galois representations