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An algebro-geometric approach to profinite iterated monodromy groups

  • Daniel Tedeschi
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Abstract

We carefully construct the profinite iterated monodromy group of a rational map as a quotient of the étale fundamental group of the punctured projective line. In doing so, we prove a number of folklore results regarding profinite IMGs; in particular, their topological generation by inertia concentrated in the post-critical orbit, and their relationship with the discrete iterated monodromy group over ℂ.

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Cite

BibTeXRIS
BibTeX
@misc{tedeschi2026algebrogeometric,
  title = {{An algebro-geometric approach to profinite iterated monodromy groups}},
  author = {Daniel Tedeschi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19117},
  eprint = {2610.19117},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19117},
}
RIS
TY  - UNPB
TI  - An algebro-geometric approach to profinite iterated monodromy groups
AU  - Daniel Tedeschi
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.19117
UR  - https://arxiv.org/abs/2610.19117
AB  - We carefully construct the profinite iterated monodromy group of a rational map as a quotient of the étale fundamental group of the punctured projective line. In doing so, we prove a number of folklore results regarding profinite IMGs; in particular, their topological generation by inertia concentrated in the post-critical orbit, and their relationship with the discrete iterated monodromy group over ℂ.
ER  -