Homology over trivial extensions of commutative DG algebras

Abstract

Conditions on the Koszul complex of a noetherian local ring $R$ guarantee that ${\mathrm{Tor}}_i^R(M,N)$ 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.

arXiv comment14 pages