On locally Laurent polynomial algebras

Neena Gupta
Abstract
Bass-Connell-Wright had proved that any finitely presented 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 describe a corresponding structure theorem for a ring A which is a locally Laurent polynomial algebra in n variables over an integral domain R. We shall also mention conditions for a faithfully flat algebra to be a locally Laurent polynomial algebra. For instance, any faithfully flat algebra over a Noetherian normal domain R, whose generic and codimension-one fibres are Laurent polynomial algebras in n variables, is locally Laurent polynomial. The results have been obtained in a joint work with S.M. Bhatwadekar.