Criteria for vanishing of Tor over Complete Intersections
  In this paper we exploit properties of Dao's eta-pairing as well as techniques of Huneke, Jorgensen, and Wiegand to study the vanishing of Tor_i(M,N) of finitely generated modules M, N over complete intersections. We prove vanishing of Tor_i(M, N) for all positive integers i under depth conditions on M, N, and their tensor product. Our arguments improve a result of Dao and establish a new connection between the vanishing of Tor and the depth of tensor products. 
Olgur Celikbas, Srikanth B. Iyengar, Greg Piepmeyer, and Roger Wiegand
math.AC