Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak factorization and the Grothendieck group of Deligne-Mumford stacks   We construct a presentation for the Grothendieck group of Deligne-Mumford
stacks over a field of characteristic zero. The generators for this
presentation are smooth, proper Deligne-Mumford stacks and the relations are
expressed in terms of stacky blow-ups. In the process we prove a version of the
weak factorization theorem for Deligne-Mumford stacks.

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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio