When are n-syzygy modules n-torsionfree?
  Let R be a commutative noetherian ring. We consider the question of when n-syzygy modules over R are n-torsionfree in the sense of Auslander and Bridger. Our tools include Serre's condition and certain conditions on the local Gorenstein property of R. Our main result implies the converse of a celebrated theorem of Evans and Griffith. 
Hiroki Matsui, Ryo Takahashi, and Yoshinao Tsuchiya
math.AC