Differential Complexes and Stratified Pro-Modules

TL;DR

This paper introduces stratified Pro-modules and establishes an equivalence between their derived category and Pro-differential complexes, translating Saito's result into the language of Pro-objects and comparing it with Deligne's notion of Crystal in Pro-modules.

Contribution

It defines stratified Pro-modules, introduces induced objects, and proves an equivalence of derived categories, extending Saito's equivalence into the Pro-object framework.

Findings

Established an equivalence between derived categories of stratified Pro-modules and Pro-differential complexes.

Translated Saito's Morihiko Saito equivalence into the language of Pro-objects.

Compared stratified Pro-modules with Deligne's notion of Crystal in Pro-modules.

Abstract

In this paper we introduce the category of stratified Pro-modules and the notion of induced object in this category. We propose a translation of a Morihiko Saito equivalence result using the dual language of Pro-objects. So we prove an equivalence between the derived category of stratified Pro-modules and the category of Pro-differential complexes. We also supply a comparison with the notion of Crystal in Pro-module (introduced by P. Deligne in 1960).