Filtrations of the perverse sheaf of nearby cycles in the semi stable situation

Abstract

In the strict semi stable reduction situation, we describe the various filtrations of the perverse sheaf of nearby cycles in terms of irreducible perverse sheaves together with the action of the monodromy operator. We then study the spectral sequences associated to these filtration computing the sheaf cohomology groups. Finally we propose an illustration of how it can be used to compute the cohomology groups. Considering the similarity with the results of my paper at Duke Math. Journal,, it could be a good introduction before reading loc. cit.