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A stacky resolution of singularities for orders by Azumaya algebras

  • Timothy De Deyn
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Abstract

We construct a stacky resolution of singularities for certain noncommutative spaces which can be viewed as 'finite noncommutative extensions' of schemes. More precisely, we show that any order over a reduced separated finite type scheme over a field of characteristic zero can be resolved by an Azumaya algebra over a smooth Deligne--Mumford stack by a sequence of stacky blow-ups.

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Cite

BibTeXRIS
BibTeX
@misc{deyn2026stacky,
  title = {{A stacky resolution of singularities for orders by Azumaya algebras}},
  author = {Timothy De Deyn},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.05137},
  eprint = {2606.05137},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.05137},
}
RIS
TY  - UNPB
TI  - A stacky resolution of singularities for orders by Azumaya algebras
AU  - Timothy De Deyn
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2606.05137
UR  - https://arxiv.org/abs/2606.05137
AB  - We construct a stacky resolution of singularities for certain noncommutative spaces which can be viewed as 'finite noncommutative extensions' of schemes. More precisely, we show that any order over a reduced separated finite type scheme over a field of characteristic zero can be resolved by an Azumaya algebra over a smooth Deligne--Mumford stack by a sequence of stacky blow-ups.
ER  -