A Generalization of the Auslander-Reiten Conjecture for the Bounded   Derived Category
  We study the bounded derived category $\D^b(\Rmod)$ of a left Noetherian ring $R$. We give a version of the Generalized Auslander-Reiten Conjecture for $\D^b(\Rmod)$ that is equivalent to the classical statement for the module category and is preserved under derived equivalence. 
Kosmas Diveris, Marju Purin
math.RT