# 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.

**MAR**

**13**