Tilting complexes and Auslander-Reiten conjecture.
An open problem in the theory of finitely presented modules over Artin algebras is the Auslander-Reiten conjecture which states that if \(X\) is a finitely presented module over an Artin algebra \(R\) such that \(\mathrm{Ext}^i_R(X,X\oplus R)=0\) for all \(i>0\) then \(X\) is projective. In the present paper the author proves that this conjecture is stable under derived equivalences (Theorem 4.4). In order to do this Wei develops an interesting study of self-orthogonal objects in the bounded derived category associated to a coherent ring (Section 3).
scientific article; zbMATH DE number 6097128
scientific article