**Date & Time:** Thursday, September 18, 2008, 15:00- 16:00.

**Venue:** Ramanujan Hall

**Title:** Structure of Algebras which are Locally * A^{1}* in Codimension One

**Speaker:** Amartya K. Dutta, ISI Kolkota

**Abstract:** Let *R* be a Noetherian normal domain and *A* a faithfully flat *R*-algebra
whose generic and codimension-one fibre rings are * A^{1}*
(i.e., polynomial algebras in one variable). It was observed (Dutta
1994) that if

*A*is finitely generated, then

*A*is actually the symmetric algebra of an invertible ideal of

*R*. Results of this type led to the investigation of the general structure of such algebras. For instance, it was discovered (Dutta-Onoda 2007) that if

*R*is a UFD, then

*A*can be expressed as a direct limit of polynomial algebras.

In this talk, we shall discuss the above results with examples and mention recent results in this direction obtained by Bhatwadekar-Dutta-Onoda in an ongoing investigation.