Weak factorization and the Grothendieck group of Deligne-Mumford stacks
arXiv:1707.06040 · doi:10.1016/j.aim.2018.09.030
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.
Final version
References in corpus (6)
- The Grothendieck group of algebraic stacks
- Functorial destackification of tame stacks with abelian stabilisers
- Grothendieck ring of pretriangulated categories
- Approximating classifying spaces by smooth projective varieties
- Factorization for stacks and boundary complexes
- A power structure over the Grothendieck ring of geometric dg categories