# Tate Resolutions and Maximal Cohen-Macaulay Approximations

## TL;DR

This paper explores Tate resolutions and maximal Cohen-Macaulay approximations of modules over Gorenstein rings, extending known linkage results for complete intersections.

## Contribution

It introduces new insights into the relationship between Tate resolutions and Cohen-Macaulay approximations in the context of Gorenstein rings.

## Key findings

- Extended linkage results for complete intersections.
- Established connections between Tate resolutions and Cohen-Macaulay modules.
- Provided new methods for approximating modules over Gorenstein rings.

## Abstract

We study the Tate resolutions and the maximal Cohen-Macaulay approximations of Cohen-Macaulay modules over Gorenstein rings. One consequence is an extension of a well-known result about linkage of complete intersections.