On $p$-adic differential equations on semistable varieties

TL;DR

This paper establishes a comparison theorem linking modules with integrable connections on the generic fiber of a semistable variety to log overconvergent isocrystals on its special fiber, advancing p-adic differential equations theory.

Contribution

It introduces a new comparison theorem connecting p-adic differential modules on semistable varieties with log overconvergent isocrystals, enriching the understanding of p-adic cohomology.

Findings

Proves a comparison theorem between two categories of p-adic objects.

Bridges the gap between generic fiber modules and special fiber isocrystals.

Enhances the theoretical framework for p-adic differential equations on semistable varieties.

Abstract

In this paper we prove a comparison theorem between the category of certain modules with integrable connection on the complement of a normal crossing divisor of the generic fiber of a proper semistable variety over a DVR and the category of certain log overconvergent isocystrals on the special fiber of the same open.