Lifting and restricting
        t-structures
    
    
    We explore the interplay of
        t-structures in the bounded derived category
    of finitely generated modules
        and the unbounded derived category of all
    modules over a noetherian ring
        A. More precisely, we show that every
    intermediate t-structure in
        D^b(A) lifts to a compactly generated
    t-structure in D(A), 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) to restrict to
    an intermediate t-structure in
        D^b(A). Finally, we consider the special
    case of HRS-t-structures and
        discuss applications to silting theory.
    This talk is based on joint work
      with Alexandra Zvonareva.