  This works concerns cohomological support varieties of modules over
commutative local rings. The main result is that the support of a derived
tensor product of a pair of differential graded modules over a Koszul complex
is the join of the supports of the modules. This generalizes, and gives another
proof of, a result of Dao and the third author dealing with Tor-independent
modules over complete intersection rings. The result for Koszul complexes has a
broader applicability, including to exterior algebras over local rings.
