We consider the homotopy category of complexes of projective modules over a
Noetherian ring. Truncation at degree zero induces a fully faithful triangle
functor from the totally acyclic complexes to the stable derived category. We
show that if the ring is either Artin or commutative Noetherian local, then the
functor is dense if and only if the ring is Gorenstein. Motivated by this, we
define the Gorenstein defect category of the ring, a category which in some
sense measures how far the ring is from being Gorenstein.Comment: 11 pages, updated versio