Vanishing of Tor Over Complete Intersections

Abstract

In this paper we are concerned with the vanishing of $\text{Tor}$ over complete intersection rings. Building on results of C. Huneke, D. Jorgensen and R. Wiegand, and, more recently, H. Dao, we obtain new results showing that good depth properties on the $R$-modules $M$, $N$ and $M{\otimes }_{R}N$ force the vanishing of ${\text{Tor}}_i^R(M,N)$ for all $i\ge 1$.

25 pages, to appear in the Journal of Commutative Algebra

Cited by in corpus (5)

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• Bounds on depth of tensor products of modules
• Syzygies and tensor product of modules
• On the vanishing of theta invariant and a conjecture of Huneke and Wiegand