REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

Sean Sather-Wagstaff

ABSTRACT:  Huneke has asked whether a local Cohen-Macaulay ring R whose Bass numbers are eventually constant must be Gorenstein. We will show how the existence of a nontrivial semidualizing R-module implies that the Bass numbers of R must grow at least linearly; moreover, the existence of a chain of d+1 semidualizing modules yield a degree d polynomial lower bound for the Bass numbers of R. Furthermore, we show how information about the first few Bass numbers of R yields information about the structure of the class of semidualizingR-modules.