Date & Time: Thursday, September 18, 2008, 15:00- 16:00.
Venue: Ramanujan Hall

Title: Structure of Algebras which are Locally A1 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 A1 (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.