# Cotilting with balanced big Cohen-Macaulay modules

## TL;DR

This paper classifies certain cotilting classes over Cohen-Macaulay rings with canonical modules, focusing on balanced big Cohen-Macaulay modules and their relations to local cohomology and Gorenstein flat modules.

## Contribution

It provides a classification of d-cotilting classes containing balanced big Cohen-Macaulay modules and explores their connections with local cohomology and Gorenstein flat modules.

## Key findings

- Classified d-cotilting classes containing balanced big Cohen-Macaulay modules.
- Identified the smallest and largest cotilting classes related to modules of depth d.
- Analyzed the interplay between local cohomology, canonical duality, and cotilting modules.

## Abstract

Over $d$-dimensional Cohen-Macaulay rings with a canonical module, $d$-cotilting classes containing the maximal and balanced big Cohen-Macaulay modules are classified. Particular emphasis is paid to the direct limit closure of the balanced big Cohen-Macaulay modules, and the class of modules of depth $d$, which are shown to respectively be the smallest and largest such cotilting classes. Considerations are then given to the interplay between local cohomology, canonical duality and cotilting modules for the class of Gorenstein flat modules over Gorenstein local rings.