Mixed tate motives and the unit equation II

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6 Scopus citations


Over the past fifteen years or so, Minhyong Kim has developed a framework for making effective use of the fundamental group to bound (or even compute) integral points on hyperbolic curves. This is the third installment in a series whose goal is to realize the potential effectivity of Kim’s approach in the case of the thrice punctured line. As envisioned by Dan-Coehn and Wewers (2016), we construct an algorithm whose output upon halting is provably the set of integral points, and whose halting would follow from certain natural conjectures. Our results go a long way towards achieving our goals over the rationals, while broaching the topic of higher number fields.

Original languageEnglish
Pages (from-to)1175-1237
Number of pages63
JournalAlgebra and Number Theory
Issue number5
StatePublished - 1 Jan 2020


  • Integral points
  • Mixed Tate motives
  • P-adic periods
  • Polylogarithms
  • Unipotent fundamental group
  • Unit equation

ASJC Scopus subject areas

  • Algebra and Number Theory


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