The Auslander Bound for Complexes

If a module $M$ has finite projective dimension, then the Ext modules of $M$ against any other module eventually vanish and the projective dimension of $M$ gives a uniform bound for this vanishing. For modules of infinite projective dimension there can still exist a bound. Such a bound is called the Auslander bound. In this paper we define a similar bound for complexes and give applications.