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Algebra Seminar: Kamran Divaani-Aazar, Alzahra University, Iran

Speaker: Kamran Divaani-Aazar, Alzahra University, Iran

Title: A Gorenstein analogue of the New Intersection Theorem

Abstract: Let (R,m,k) be a local ring. The celebrated New Intersection theorem implies many other
intersection theorems. Also, it yields Bass's conjecture and Auslander's Zero-divisor conjecture. There is
much evidence supporting Holm’s claim: “Every result in Classical Homological Algebra should have a counterpart
in Gorenstein Homological Algebra”. Thus, it is natural to look for a Gorenstein analogue of the New Intersection
theorem.

In this talk, we first review the New Intersection theorem and some of its immediate implications. Then, we
establish a Gorenstein analogue of the New Intersection theorem, when R is a quasi-specialization of a
G-regular local ring.

This talk is based on a joint work with Fatemeh Mohammadi Aghjeh Mashhad, Ehsan Tavanfar and Massoud Tousi.

To attend virtually, send a request to Dr. Ela Celikbas or Dr. Olgur Celikbas.