Indecomposables with smaller cohomological length in the derived   category of gentle algebras
  Bongartz and Ringel proved that there is no gaps in the sequence of lengths of indecomposable modules for the finite-dimensional algebras over algebraically closed fields. The present paper mainly study this "no gaps" theorem for the bounded derived module category $D^b(A)$ of a gentle algebra $A$: if there is an indecomposable object in $D^b(A)$ of cohomological length $l>1$, then there exists an indecomposable with cohomological length $l-1$. 
Chao Zhang
math.RT math.RA