Commutative Algebra seminar
Speaker: Samarendra Sahoo (IIT Bombay)
Host: Tony Puthenpurakal
Title: The Auslander-Reiten Conjecture
Time, day and date: 4:00:00 PM, Tuesday, March 18
Venue: Ramanujan Hall
Abstract: The Auslander-Reiten conjecture, proposed in 1975, states that if Ext^i(M,M)=Ext^i(M,R)=0 for all i≥1, then the finitely generated module M over a commutative ring R with unity must be projective. Although the conjecture remains unresolved, several partial results have been established. Notably, it holds true when R is a complete intersection (CI) or a Cohen-Macaulay (CM) normal ring. In this lecture series, we will explore the work of D. Ghosh and R. Takahashi, who identified a specific class of modules that satisfy the conjecture.