The Mayer-Vietoris principle for Grothendieck-Witt groups of schemes

Details The Mayer-Vietoris principle for Grothendieck-Witt groups of schemes The Mayer-Vietoris principle for Grothendieck-Witt groups of schemes

2008-11-28

arxiv.org/abs/0811.4632v1

Mathematics

K-Theory and Homology

Scientific paper

We prove localization and Zariski-Mayer-Vietoris for higher Grothendieck-Witt groups, alias hermitian $K$-groups, of schemes admitting an ample family of line-bundles. No assumption on the characteristic is needed, and our schemes can be singular. Along the way, we prove additivity, fibration and approximation theorems for the hermitian $K$-theory of exact categories with weak equivalences and duality.

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