UTA Department of Mathematics

Joint Algebra and AGANT Seminar

Date/Time/Room: Friday (2/25/2005) at 4:00pm in 487 Pickard Hall

Speaker: Dr. David A. Jorgensen
Assistant Professor of Mathematics
Department of Mathematics, University of Texas at Arlington

"On Constructions of Unliftable Modules"

Abstract: Let R=S/(x) where S is a local (commutative) ring and x is a non-zerodivisor in the square of the maximal ideal of S. Suppose M is a finitely generated R-module. Then M is said to lift to S if there exists a finitely generated S-module M' such that x is regular on M' and M is isomorphic to M'/xM'. The lifting problem is that of determining whether a given R-module lifts to S. The geometric interpretation of the lifting problem is as follows: let X be the hypersurface in ambient space corresponding to x and W a subvariety of X. Then does there exist a subvariety Y of the ambient space such that W is the intersection of X and Y, and the dimension of Y is one more than the dimension of W? In this talk, which constitutes joint work with A.J Todd, we give a general construction of unliftable modules of finite projective dimension.