Sarang Sharad Sane

We consider bounded complexes P• of finitely generated projective A-modules whose homologies have finite projective dimension and are locally Cohen-Macaulay. We give a necessary and sufficient condition so that its dual P•* also has the same property.

For a Cohen-Macaulay ring R, we exhibit the equivalence of the bounded derived categories of certain resolving subcategories, which, amongst other results, yields an equivalence of the bounded derived category of finite length and finite projective dimension modules with the bounded derived category of projective modules with finite length homologies. This yields isomor-phisms of K-theory and Witt groups (amongst other invariants) and improves on terms of associated spectral sequences and Gersten complexes.

In this paper we extend and apply the work of Paul Balmer and others on derived and triangular Witt Groups. We obtain a generalized form of dévissage for derived Witt Groups over Cohen-Macaulay rings. 2000 Mathematics Subject Classification: Primary: 11E81, 18E30, 19G12; Secondary: 13C10, 13D.