| It is proved that the minimal free resolution of a module M over a Gorenstein local ring R is eventually periodic if, and only if, the class of M is torsion in a certain Z [t+/-1]-associated to R. This module, denoted J(R), is the free Z [t+/-1]-module on the isomorphism classes of finitely generated R-modules modulo relations reminiscent of those defining the Grothendieck group of R. The main result is a structure theorem for J(R) when R is a complete Gorenstein local ring; the link between periodicity and torsion stated above is a corollary. |
