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

TL;DR

This paper analyzes the filtrations of the perverse sheaf of nearby cycles in semi-stable reduction, detailing their structure, associated spectral sequences, and applications to computing sheaf cohomology groups.

Contribution

It provides a detailed description of filtrations of nearby cycles in semi-stable situations and explores their spectral sequences and computational applications.

Findings

Filtrations expressed via irreducible perverse sheaves and monodromy.

Spectral sequences computed for sheaf cohomology.

Method demonstrated for calculating cohomology groups.

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.