A silting theorem

Abstract

We give a generalization of the classical tilting theorem of Brenner and Butler. We show that for a 2-term silting complex P in the bounded homotopy category Kb(projA) of finitely generated projective modules of a finite dimensional algebra A, the algebra B=EndKb(projA)(P) admits a 2-term silting complex Q with the following properties: (i) The endomorphism algebra of Q in Kb(projB) is a factor algebra of A, and (ii) there are induced torsion pairs in modA and modB, such that we obtain natural equivalences induced by Hom- and Ext-functors. Moreover, we show how the Auslander–Reiten theory of modB can be described in terms of the Auslander–Reiten theory of modA.