Linkage of finite GC-dimension modules

Let R be a semiperfect commutative Noetherian ring and C a semidualizing R-module. We study the theory of linkage for modules of finite GC-dimension. For a horizontally linked R-module M of finite GC-dimension, the connection of the Serre condition (Sn) with the vanishing of certain relative cohomology modules of its linked module is discussed.