Linkage of modules over Cohen–Macaulay rings

Abstract

Inspired by the theory of linkage for ideals, the concept of sliding depth of a finitely generated module over a Noetherian local ring is defined in terms of its Ext modules. As a result, in the module-theoretic linkage theory of Martsinkovsky and Strooker, one proves the Cohen–Macaulayness of a linked module if the base ring is Cohen–Macaulay (not necessarily Gorenstein). Some interplay is established between the sliding depth condition and other module-theoretic notions such as the G-dimension and the property of being sequentially Cohen–Macaulay.