School of Mathematics Colloquium
On locally Laurent polynomial algebras
by Dr. Neena Gupta (TIFR)
Thursday, July 19, 2012
from
to
(Asia/Kolkata)
at Colaba Campus ( AG-69 )
at Colaba Campus ( AG-69 )
Description |
In 1977, Bass, Connell and Wright established that any finitely generated locally polynomial algebra in n variables over an integral domain R is isomorphic to the symmetric algebra of a finitely generated projective R-module of rank n. In this talk, we shall present an analogous structure theorem for any R-algebra which is locally a Laurent polynomial algebra in n variables. Next we shall give sufficient conditions for a faithfully flat R-algebra A to be a locally Laurent polynomial algebra. We shall see that over a discrete valuation ring R any Laurent polynomial fibration is necessarily a Laurent polynomial algebra. We shall then consider fibre conditions over more general domains. If time permits, we shall also mention a few results on the structure of certain algebras whose generic fibres are {\mathbb A}^*. The results have been obtained jointly with S.M. Bhatwadekar. |