Vanishing of Tor Over Complete Intersections

Details Vanishing of Tor Over Complete Intersections Vanishing of Tor Over Complete Intersections

2009-04-08

arxiv.org/abs/0904.1408v3

Mathematics

Commutative Algebra

25 pages, to appear in the Journal of Commutative Algebra

Scientific paper

In this paper we are concerned with the vanishing of $\textnormal{Tor}$ 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 $M\otimes_RN$ force the
vanishing of $\textnormal{Tor}^{R}_{i}(M,N)$ for all $i\geq 1$.

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