# Hasse--Schmidt modules versus integrable connections

## TL;DR

This paper demonstrates that in characteristic zero, Hasse-Schmidt modules are equivalent to modules with integrable connections, showing that the former can be fully recovered from the latter.

## Contribution

It establishes the equivalence between Hasse-Schmidt modules and modules with integrable connections in characteristic zero, clarifying their relationship.

## Key findings

- Hasse-Schmidt modules can be recovered from integrable connections in characteristic zero
- Hasse-Schmidt modules and modules with integrable connections are equivalent in characteristic zero
- The result simplifies the understanding of module structures in algebraic geometry

## Abstract

We prove that, in characteristic 0, any Hasse-Schmidt module structure can be recovered from its underlying integrable connection, and consequently Hasse--Schmidt modules and modules endowed with an integrable connection coincide.