**Date & Time:** Tuesday, November 11, 2014, 15:30-17:00.

**Venue:** Ramanujan Hall

**Title:** Two theorems and a question of Auslander - VII

**Speaker: ** Ananthnarayan Hariharan, IIT Bombay

**Abstract:** In this series of talks, we first see a couple of theorems (one
proved by Auslander and
Goldman in 1960 and the other by Auslander in 1962), which show that a
finitely generated reflexive
module M over a regular local ring R, is free when the R-module End(M) is
either free or a finite direct
sum of copies of $M$.
Auslander asked whether this can be generalized to modules of finite
projective dimension over
Noetherian local rings. Braun (in 2004) gave a positive answer to this when
End(M) is free, using many
techniques from non-commutative algebra. We will give a simplified proof of
Braun's result which
minimises these techniques.