Vanishing of Tor Over Complete Intersections

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 $i\geq 1$.Comment: 25 pages, to appear in the Journal of Commutative Algebr

Equivalences from tilting theory and commutative algebra from the adjoint functor point of view

We give a category theoretic approach to several known equivalences from (classic) tilting theory and commutative algebra. Furthermore, we apply our main results to establish a duality theory for relative Cohen-Macaulay modules in the sense of Hellus, Schenzel, and Zargar.Comment: This is the final version (17 pages) to appear in the New York Journal of Mathematic