Jordan H\"older theorems for derived module categories of piecewise   hereditary algebras
  A Jordan H\"older theorem is established for derived module categories of piecewise hereditary algebras. The resulting composition series of derived categories are shown to be independent of the choice of bounded or unbounded derived module categories, and also of the choice of finitely generated or arbitrary modules. 
Lidia Angeleri H\"ugel, Steffen Koenig, Qunhua Liu
math.RT math.RA