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 presentatio...

TILTING THEORY FOR QUIVERS AND RELATED CATEGORIES MORITZ GROTH AND JAN ŠŤOVÍČEK Abstract. We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between the corresponding representation theories with values in arbitrary s...

Abstract Building on work of Gerstenhaber, we show that the space integrable derivations an Artin algebra forms a Lie algebra, and restricted if contains field characteristic . We deduce classes in (restricted) is invariant under derived equivalences, stable equivalences Morita type between self‐injective algebras. also provide negative answers to questions about posed by Linckelmann Farkas, Ge...

We consider derived categories of coherent sheaves on smooth projective varieties. We prove that any equivalence between them can be represented by an object on the product. Using this, we give a necessary and sufficient condition for equivalence of derived categories of two K3 surfaces.

We interpret Hochschild cohomology as the Lie algebra of the derived Picard group and deduce that it is preserved under derived equivalences.

It is about a decade since Broué made his celebrated conjecture [2] on equivalences of derived categories in block theory: that the module categories of a block algebra A of a finite group algebra and its Brauer correspondent B should have equivalent derived categories if their defect group is abelian. Since then, character-theoretic evidence for the conjecture has accumulated rapidly, but unti...

We generalize derived equivalences for triangular matrix rings induced by a certain type of classical tilting module introduced by Auslander, Platzeck and Reiten to generalize reflection functors in the representation theory of quivers due to Bernstein, Gelfand and Ponomarev.