Let $A$ be a hereditary algebra and let $\mathcal{D}$ be the derived category of bounded complex of finitely generated $A$-modules. Then, for any complex $C\_{\bullet}$ in $\mathcal{D}$, we have $C\_{\bullet} \cong H\_{\bullet}(C\_{\bullet})$, where the right hand side is the complex whose $i$-th term is $H\_i(C\_{\bullet})$ and all of whose maps are zero.


I would like to know a standard reference for this. Ideally, I would like to know the original source.


Right now, the only sources I know are lecture notes, such as Section 2.5 of [Keller's notes](http://www.math.jussieu.fr/~keller/ictp2006/lecturenotes/keller.pdf) or Theorem 2.1 in [Lenzing's](http://www.math.jussieu.fr/~keller/ictp2006/lecturenotes/lenzing1.pdf).


Thanks!



Earliest/most standard reference for derived categories of hereditary algebras
Dieter Happel's [book](http://www.ams.org/mathscinet-getitem?mr=935124) *Triangulated Categories in the representation theory of finite dimensional algebras* is a pretty canonical source, and it includes the result you mention.


(That particular result might be folkloric, though)


