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, April 08
Venue: Ramanujan Hall
Abstract: The Auslander-Reiten conjecture, proposed in 1975, states that if Exti(M,M)=Exti(M,R)=0 for all i≥1, then a finitely generated module M over a Noetherian commutative ring R must be projective. In the last two lectures, we discussed how the conjecture holds if the injective dimension of Hom(M,M) or Hom(M,R) is finite. In the next lecture, we will examine a result by T. Araya, which states that for Gorenstein rings, it suffices to verify the conjecture for rings of dimension at most one. If time permits, we will also discuss recent work by D. Ghosh and M. Samanta on the finite complete intersection dimension of M and Hom(M,R).