Commutative Algebra Seminar

Title

Remarks on the total reflexivity for modules

Abstract

The notion of totally reflexive module has been introduced by Auslander and Bridger. A finitely generated module M over a noetherian ring R is called “totally reflexive” if the following two conditions are satisfied:

(1) Ext^i_R(M,R)=0 for all i>0, (2) Ext^i_R(Tr(M),R)=0 for all i>0.

Here, Tr(M) is the Auslander transpose of M. There is a famous question that “Does the condition (1) imply the condition (2)?”. In 2004, D. Jorgensen and L. Sega gave a counter example. However, there are many cases where the question is hold. In this talk, we will consider when the question is hold.