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Conditions on the Koszul complex of a noetherian local ring $R$ guaranteethat $\mathrm{Tor}^{R}_{i}(M,N)$ 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 differentialgraded modules over certain trivial extensions of commutative differentialgraded algebras.

Homology over trivial extensions of commutative DG algebras