A 2003 counterexample to a conjecture of Auslander brought attention to a family
of rings—colloquially called AC rings—that satisfy a natural condition on vanishing of
cohomology. Several results attest to the remarkable homological properties of AC rings, but their definition is barely operational, and it remains unknown if they form a class that is closed under typical constructions in ring theory. In this paper, we study transfer of the AC property along local homomorphisms of Cohen–Macaulay rings. In particular, we show that the AC property is preserved by standard procedures in local algebra. Our results also yield new examples of Cohen–Macaulay AC rings.