DMS Algebra Seminar

Speaker: Justin Lyle (Auburn)

Title: Vanishing of Tor and Depth of Tensor Products

Abstract: Let \(R\) be a commutative Noetherian local ring and let \(M,N\) be finitely generated \(R\)-modules. A classical problem is to calculate the depth of the tensor product of \(M\) and \(N\). This turns out to be extremely difficult to do, even under very stringent hypotheses. In this talk, we will discuss some classical work of Auslander, Huneke-Wiegand, Iyengar, and others on this problem, before moving on to discuss recent works of the speaker giving characterizations for rings over which depth of tensor products always behaves "nicely."

This talk is based primarily on joint work with Kaito Kimura and Andrew Soto Levins.