  Conditions on the Koszul complex of a noetherian local ring $R$ guarantee
that $\mathrm{Tor}^{R}_{i}(M,N)$ is non-zero for infinitely many $i$, when $M$
and $N$ are finitely generated $R$-modules of infinite projective dimension.
These conditions are obtained from results concerning Tor of differential
graded modules over certain trivial extensions of commutative differential
graded algebras.
