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.