Lifting and restricting t‐structures

Abstract

AbstractWe explore the interplay between t‐structures in the bounded derived category of finitely presented modules and the unbounded derived category of all modules over a coherent ring using homotopy colimits. More precisely, we show that every intermediate t‐structure in can be lifted to a compactly generated t‐structure in , by closing the aisle and the coaisle of the t‐structure under directed homotopy colimits. Conversely, we provide necessary and sufficient conditions for a compactly generated t‐structure in to restrict to an intermediate t‐structure in , thus describing which t‐structures can be obtained via lifting. We apply our results to the special case of HRS‐t‐structures. Finally, we discuss various applications to silting theory in the context of finite dimensional algebras.