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PreprintCC BY 4.0arXiv

Existence of coarse moduli superspaces for Deligne--Mumford superstacks

  • Fei Peng
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Abstract

We prove that every Deligne--Mumford superstack over ℤ[1/2] with finite inertia admits a coarse moduli superspace. This generalizes the Keel--Mori theorem to the super setting. As part of our argument, we introduce a notion of integral morphisms in algebraic supergeometry and use it to establish an effective descent result for étale morphisms of algebraic superspaces. We also include an example of a non-Deligne--Mumford superstack with finite inertia that does not admit a coarse moduli superspace.

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Cite

BibTeXRIS
BibTeX
@misc{peng2026existence,
  title = {{Existence of coarse moduli superspaces for Deligne--Mumford superstacks}},
  author = {Fei Peng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25524},
  eprint = {2609.25524},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25524},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Existence of coarse moduli superspaces for Deligne--Mumford superstacks
AU  - Fei Peng
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.25524
UR  - https://arxiv.org/abs/2609.25524
AB  - We prove that every Deligne--Mumford superstack over ℤ[1/2] with finite inertia admits a coarse moduli superspace. This generalizes the Keel--Mori theorem to the super setting. As part of our argument, we introduce a notion of integral morphisms in algebraic supergeometry and use it to establish an effective descent result for étale morphisms of algebraic superspaces. We also include an example of a non-Deligne--Mumford superstack with finite inertia that does not admit a coarse moduli superspace.
ER  -