Subcategories of the derived category and cotilting complexes (Q2717700)

There is a beautiful one-to-one correspondence between basic cotilting modules over an Artin algebra \(\Lambda\) and certain contravariantly finite subcategories of the category \(\text{mod }\Lambda\) of finitely generated \(\Lambda\)-modules [\textit{M. Auslander} and \textit{I. Reiten}, Adv. Math. 86, No. 1, 111-152 (1991; Zbl 0774.16006)]. In the paper under review, a triangulated version of this correspondence for the bounded derived category \(D^b(\text{mod }\Lambda)\) is discussed. More precisely, the author proves a one-to-one correspondence between basic cotilting complexes and certain contravariantly finite subcategories of \(D^b(\text{mod }\Lambda)\). This is used to give a criterion for the existence of complements to exceptional complexes.