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PreprintCC BY 4.0arXiv

Fundamental groups of proper algebraic stacks are finitely presented

  • Chirantan Chowdhury
  • Ludvig Modin
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Abstract

Lara, Srinivas and Stix showed that the étale fundamental group of a proper scheme over an algebraically closed field is topologically finitely presented. Building on this, we show that the étale fundamental group, as introduced by Noohi, of a proper algebraic stack with finite inertia over an algebraically closed field is topologically finitely presented.

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Cite

BibTeXRIS
BibTeX
@misc{chowdhury2026fundamental,
  title = {{Fundamental groups of proper algebraic stacks are finitely presented}},
  author = {Chirantan Chowdhury and Ludvig Modin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17255},
  eprint = {2609.17255},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17255},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Fundamental groups of proper algebraic stacks are finitely presented
AU  - Chirantan Chowdhury
AU  - Ludvig Modin
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17255
UR  - https://arxiv.org/abs/2609.17255
AB  - Lara, Srinivas and Stix showed that the étale fundamental group of a proper scheme over an algebraically closed field is topologically finitely presented. Building on this, we show that the étale fundamental group, as introduced by Noohi, of a proper algebraic stack with finite inertia over an algebraically closed field is topologically finitely presented.
ER  -