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The general dĂ©vissage theorem for Witt groups of schemes. (English) Zbl 1175.19001
Let \(\pi:Z \to X\) be a closed subscheme of a noetherian scheme \(X\) and suppose that \(X\) has a dualizing complex \({\mathcal I}_\bullet\). The author shows that there is a dualizing complex \(\pi^\sharp{\mathcal I}_\bullet\) for \(Z\) and derives a transfer isomorphism of coherent Witt groups \(\widetilde{W}^i(Z, \pi^\sharp{\mathcal I}_\bullet) \backsimeq \widetilde{W}^i_Z(X,{\mathcal I}_\bullet)\) for all integers \(i\). The author discusses the applications of his result to regular schemes of finite Krull dimension.

MSC:
19G12 Witt groups of rings
11E81 Algebraic theory of quadratic forms; Witt groups and rings
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