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PreprintarXiv licencearXiv

Mixed Tate Chabauty--Kim beyond the polylog quotient

  • David Corwin
  • Ishai Dan-Cohen
  • Martin Lüdtke
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Abstract

We develop an algorithmic approach to mixed Tate Chabauty--Kim theory for the full unipotent fundamental group of ℙ1 smallsetminus {0,1,∞}, beyond the polylogarithmic quotient used in previous work. The key step is computing the cocycle evaluation map in the presence of a nontrivial motivic Galois action, using relations among motivic multiple zeta values. This yields explicit Kim functions involving multiple polylogarithms, as well as an algorithm for solving the S-unit equation whose halting is implied by certain natural conjectures.

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Cite

BibTeXRIS
BibTeX
@misc{corwin2026mixed,
  title = {{Mixed Tate Chabauty--Kim beyond the polylog quotient}},
  author = {David Corwin and Ishai Dan-Cohen and Martin Lüdtke},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25365},
  eprint = {2610.25365},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25365},
}
RIS
TY  - UNPB
TI  - Mixed Tate Chabauty--Kim beyond the polylog quotient
AU  - David Corwin
AU  - Ishai Dan-Cohen
AU  - Martin Lüdtke
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25365
UR  - https://arxiv.org/abs/2610.25365
AB  - We develop an algorithmic approach to mixed Tate Chabauty--Kim theory for the full unipotent fundamental group of ℙ^1 smallsetminus {0,1,∞}, beyond the polylogarithmic quotient used in previous work. The key step is computing the cocycle evaluation map in the presence of a nontrivial motivic Galois action, using relations among motivic multiple zeta values. This yields explicit Kim functions involving multiple polylogarithms, as well as an algorithm for solving the S-unit equation whose halting is implied by certain natural conjectures.
ER  -