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Nonabelian Chabauty for the Thrice-punctured Line over Cyclotomic Fields

  • Minhyong Kim
  • Xiang Li
  • Martin Lüdtke
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Abstract

In this paper we study the motivic Chabauty--Kim method, which aims to determine the set of S-integral points of ℙ1smallsetminus {0,1,∞}, over cyclotomic fields. We focus on the case K=ℚ(ζ8) and S={(1−ζ8)}, where we obtain explicit polylogarithmic Kim functions up to depth $4$ and verify Kim's Conjecture for several primes. We also observe and explain that the Chabauty--Kim locus for the polylogarithmic quotient contains, in addition to the S-integral points, certain exceptional points arising from roots of unity in ℚp.

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Cite

BibTeXRIS
BibTeX
@misc{kim2026nonabelian,
  title = {{Nonabelian Chabauty for the Thrice-punctured Line over Cyclotomic Fields}},
  author = {Minhyong Kim and Xiang Li and Martin Lüdtke},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01128},
  eprint = {2609.01128},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01128},
}
RIS
TY  - UNPB
TI  - Nonabelian Chabauty for the Thrice-punctured Line over Cyclotomic Fields
AU  - Minhyong Kim
AU  - Xiang Li
AU  - Martin Lüdtke
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.01128
UR  - https://arxiv.org/abs/2609.01128
AB  - In this paper we study the motivic Chabauty--Kim method, which aims to determine the set of S-integral points of ℙ^1smallsetminus {0,1,∞}, over cyclotomic fields. We focus on the case K=ℚ(ζ_8) and S={(1−ζ_8)}, where we obtain explicit polylogarithmic Kim functions up to depth $4$ and verify Kim's Conjecture for several primes. We also observe and explain that the Chabauty--Kim locus for the polylogarithmic quotient contains, in addition to the S-integral points, certain exceptional points arising from roots of unity in ℚ_p.
ER  -