# Deformation theory of Cohen-Macaulay approximation

## TL;DR

This paper investigates the deformation theory of Cohen-Macaulay approximations, focusing on the properties of induced maps of deformation functors and establishing conditions for smoothness and injectivity.

## Contribution

It extends previous work by analyzing the deformation functors of Cohen-Macaulay approximations and deriving new cohomological conditions for their properties.

## Key findings

- Conditions for smoothness of deformation maps
- Injectivity criteria under cohomological assumptions
- Enhanced understanding of Cohen-Macaulay approximation deformations

## Abstract

In a previous article (J. Algebra 367 (2012), 142-165) we established axiomatic parametrised Cohen-Macaulay approximation which in particular was applied to pairs consisting of a finite type flat family of Cohen-Macaulay rings and modules. In this sequel we study the induced maps of deformation functors and deduce properties like smoothness and injectivity under general, mainly cohomological conditions on the module.