Duality for a Cohen-Macaulay local ring

TL;DR

This paper explores duality properties in Cohen-Macaulay local rings, extending known results to cases without canonical modules and providing new characterizations of Gorenstein modules and Cohen-Macaulay modules.

Contribution

It generalizes duality results to Cohen-Macaulay rings lacking canonical modules and offers new characterizations of Gorenstein and Cohen-Macaulay modules.

Findings

Extended duality results to rings without canonical modules

Characterizations of complete big Cohen-Macaulay modules of finite injective dimension

New criteria for Gorenstein modules over the dic completion

Abstract

Let $(R,\fm)$ be a Cohen-Macaulay local ring. If $R$ has a canonical module, then there are some interesting results about duality for this situation. In this paper, we show that one can indeed obtain similar these results in the case $R$ has not a canonical module. Also, we give some characterizations of complete big Cohen-Macaulay modules of finite injective dimension and by using it some characterizations of Gorenstein modules over the $\fm$-adic completion of $R$ are obtained.