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Triangular Witt groups. II: From usual to derived. (English) Zbl 1004.18010
This is a sequel to Part I [P. Balmer, K-Theory 19, No. 4, 311-363 (2000; Zbl 0953.18003)]. The objective is ‘linking the abstract results of Part I to classical questions for the usual Witt group’. The main result says that the derived Witt group is isomorphic to the usual Witt group when 2 is invertible. Here the usual Witt group is a generalization of Knebusch’s Witt group for algebraic varieties to the context of exact categories, and the derived Witt group is the Witt group of the derived category. The derived Witt group is one of the family of the shifted Witt groups indexed by the integers and subject to 4-periodicity. For a commutative local ring with 2 invertible the shifted Witt groups are all trivial except for the \(W^0\) which is the usual Witt group.

MSC:
18E30 Derived categories, triangulated categories (MSC2010)
19G12 Witt groups of rings
11E81 Algebraic theory of quadratic forms; Witt groups and rings
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