Modules of G-dimension zero over local rings of depth two

Abstract

Let R be a commutative noetherian local ring. Denote by mod R the category of finitely generated R-modules, and by script G sign(R) the full subcategory of mod R consisting of all R-modules of G-dimension zero. Suppose that R is henselian and non-Gorenstein, and that there is a non-free R-module in script G sign(R). Then it is known that script G sign(R) is not contravariantly finite in mod R if R has depth at most one. In this paper, we prove that the same statement holds if R has depth two. © 2004 University of Illinois.