An Auslander-Reiten principle in derived categories

Maiko Ono and Yuji Yoshino

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 of Pure and Applied Algebra

221

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