  We introduce syzygies for derived categories and study their properties.
Using these, we prove the derived invariance of the following classes of artin
algebras: (1) syzygy-finite algebras, (2) Igusa-Todorov algebras, (3) AC
algebras, (4) algebras satisfying the finitistic Auslander conjecture, and (5)
algebras satisfying the generalized Auslander-Reiten conjecture. In particular,
Gorenstein CM-finite algebras are derived invariants.
