  Support and rank varieties of modules over a group algebra of an elementary
abelian p-group have been well studied. In particular, Avrunin and Scott showed
that in this setting, the rank and support varieties are equivalent. Avramov
and Buchweitz proved an analogous result for pairs of modules over arbitrary
commutative local complete intersection rings. In this paper we study support
and rank varieties in the triangulated category of totally acyclic chain
complexes over a complete intersection ring and show that these varieties are
also equivalent.
