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The general dévissage 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
##### Keywords:
coherent Witt groups; devissage; noetherian schemes
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