Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Mayer-Vietoris principle for Grothendieck-Witt groups of schemes   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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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio