We give a principle in derived categories, which lies behind the classical Auslander-Reiten duality and its generalized version by Iyama and Wemyss. We apply the principle to show the validity of the Auslander-Reiten conjecture over a Gorenstein ring in the case where the ring has dimension larger than two and the singular locus has at most one dimension.
|Journal||Journal of Pure and Applied Algebra|
|Publication status||Published - May 15 2018|
- 13D09, 13C14, 16G50