The Gorenstein defect category
Category Theory
2014-06-05 v2 Commutative Algebra
Rings and Algebras
Abstract
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.
Cite
@article{arxiv.1202.2876,
title = {The Gorenstein defect category},
author = {Petter Andreas Bergh and David A. Jorgensen and Steffen Oppermann},
journal= {arXiv preprint arXiv:1202.2876},
year = {2014}
}
Comments
11 pages, updated version