Tuesday, November 3, 2020

Frederik Marks, Lifting and restricting t-structures

Abstract:
Given a noetherian ring A, we show that every intermediate t-structure in the bounded derived category D^b(A-mod) lifts to a compactly generated t-structure in the unbounded derived category D(A-Mod), by closing the respective classes under directed homotopy colimits. Conversely, we provide necessary and sufficient conditions for a compactly generated t-structure in D(A-Mod) to restrict to an intermediate t-structure in D^b(A-mod). Finally, we discuss applications to silting theory and consider the special case of HRS-t-structures, thus establishing a link to torsion pairs in module categories. This talk is based on joint work with Alexandra Zvonareva.