Limits of weight filtrations and limits of slope filtrations on infinitesimal cohomologies in mixed characteristics I

Abstract

In this book we construct fundamental filtered complexes in filtered derived categories. These are generalizations of a filtered complex constructed by Mokrane. As an application of these constructions, we develop theory of limits of weight filtrations and limits of slope filtrations on the infinitesimal cohomologies of proper smooth schemes over the fraction field of a complete discrete valuation ring of mixed characteristics with perfect residue field.