# A non-commutative differential module approach to Alexander modules

## TL;DR

This paper introduces a novel approach to Alexander modules using non-commutative differential modules, drawing analogies with cotangent complexes and illustrating with Galois covering examples.

## Contribution

It develops a non-commutative differential module framework for Alexander modules, extending Crowell's derived modules and connecting to cotangent complex theory.

## Key findings

- New non-commutative differential module approach to Alexander modules
- Analogies established with cotangent complex theory
- Examples from Galois coverings of curves

## Abstract

The theory of R. Crowell on derived modules is approached within the theory of non-commutative differential modules. We also seek analogies to the theory of cotangent complex from differentials in the commutative ring setting. Finally we give examples motivated from the theory of Galois coverings of curves.

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Source: https://tomesphere.com/paper/1904.06665