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A proper arithmetic surface with infinite étale fundamental group

  • Pablo Chenal
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Abstract

We give an example of a proper, regular, integral arithmetic surface over Spec Z endowed with a section, and whose étale fundamental group admits an infinite pro-$2$ quotient. The construction is a geometric analog of the Golod--Shafarevich towers for rings of integers of number fields.

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Cite

BibTeXRIS
BibTeX
@misc{chenal2026proper,
  title = {{A proper arithmetic surface with infinite étale fundamental group}},
  author = {Pablo Chenal},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05972},
  eprint = {2610.05972},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05972},
}
RIS
TY  - UNPB
TI  - A proper arithmetic surface with infinite étale fundamental group
AU  - Pablo Chenal
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.05972
UR  - https://arxiv.org/abs/2610.05972
AB  - We give an example of a proper, regular, integral arithmetic surface over Spec Z endowed with a section, and whose étale fundamental group admits an infinite pro-$2$ quotient. The construction is a geometric analog of the Golod--Shafarevich towers for rings of integers of number fields.
ER  -