Bass Numbers and Semidualizing Complexes

Details Bass Numbers and Semidualizing Complexes Bass Numbers and Semidualizing Complexes

2008-12-03

arxiv.org/abs/0812.0643v3

Mathematics

Commutative Algebra

28 pages, uses xy-pic; v.2 incorporates minor changes throughout, and discussions of semidualizing objects over non-local ring

Scientific paper

Let R be a commutative local noetherian ring. We prove that the existence of a chain of semidualizing R-complexes of length (d+1) yields a degree-d polynomial lower bound for the Bass numbers of R. We also show how information about certain Bass numbers of R provide restrictions on the lengths of chains of semidualizing R-complexes. To make this article somewhat self-contained, we also include a survey of some of the basic properties of semidualizing modules, semidualizing complexes and derived categories.

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