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Abstract: For the module category of a hereditary ring, the Ext-orthogonal pairs of subcategories are studied. For each Ext-orthogonal pair that is generated by a single module, a 5-term exact sequence is constructed. The pairs of finite type are characterized and two consequences for the class of hereditary rings are established: homological epimorphisms and universal localizations coincide, and the telescope conjecture for the derived category holds true. However, we present examples showing that neither of these two statements is true in general for rings of global dimension 2. [ABSTRACT FROM AUTHOR]

Abstract: An Auslander–Reiten formula for complexes of modules is presented. This formula contains as a special case the classical Auslander–Reiten formula. The Auslander–Reiten translate of a complex is described explicitly, and various applications are discussed. [Copyright &y& Elsevier]