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arXiv · 1707.06040

Weak factorization and the Grothendieck group of Deligne-Mumford stacks

Daniel Bergh
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Abstract

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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Daniel Bergh. 2017-07-19. Weak factorization and the Grothendieck group of Deligne-Mumford stacks. https://doi.org/10.1016/j.aim.2018.09.030

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