  We investigate the perfect derived category dgPer(A) of a positively graded
differential graded (dg) algebra A whose degree zero part is a dg subalgebra
and semisimple as a ring. We introduce an equivalent subcategory of dgPer(A)
whose objects are easy to describe, define a t-structure on dgPer(A) and study
its heart. We show that dgPer(A) is a Krull-Remak-Schmidt category. Then we
consider the heart in the case that A is a Koszul ring with differential zero
satisfying some finiteness conditions.
