Linkage of finite Gorenstein dimension modules
The modern theory of linkage for subschemes of projective space was introduced by C. Peskine and L. Szpiro in 1974, although its origins go back much farther. A great deal of work in the setting of ideals in a local ring was done most notably by C. Huneke and B. Ulrich in the 1980's. A few authors advanced the theory to the setting of linkage of modules in the 2000's, for instance U. Nagel, H. Martin, A. Martsinkovsky and J.R. Strooker, and Y. Yoshino and S. Isogawa. In particular, Martsinkovsky and Strooker define the notion of \textit{horizontal linkage} for modules. In this paper the authors study the theory of linkage for a class of modules which have finite Gorenstein dimension. For a horizontally linked module \(M\) over a commutative semiperfect Noetherian ring \(R\), they study the connections of its reduced grade, its Gorenstein dimension, and its depth. They also discuss the connection between the Serre condition \((S_n)\) on an \(R\)-module of finite Gorenstein dimension and the vanishing of the local cohomology groups of its linked module.
scientific article; zbMATH DE number 6201466