Tilting Theory for Coherent Rings and Almost Hereditary Noetherian Rings

We generalize two major ways of obtaining derived equivalences, the tilting process by Happel, Reiten and Smalø and Happel’s Tilting Theorem, to the setting of finitely presented modules over right coherent rings. Moreover, we extend the characterization of quasi–tilted artin algebras as the almost hereditary ones to all right noetherian rings. We also give a streamlined and general presentation of how to obtain derived equivalences without tilting objects, using torsion pairs instead.