Mixed Tate Motives and the Unit Equation

Ishai Dan-Cohen, Stefan Wewers

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


This is the second installment in a sequence of articles devoted to "explicit Chabauty-Kim theory" for the thrice punctured line. Its ultimate goal is to construct an algorithmic solution to the unit equation whose halting will be conditional on Goncharov's conjecture about exhaustion of mixed Tate motives by motivic iterated integrals (refined somewhat with respect to ramification), and on Kim's conjecture about the determination of integral points via p-adic iterated integrals. In this installment, we explain what this means while developing basic tools for the construction of the algorithm. We also work out an elaborate example, which goes beyond the cases that were understood before, and allows us to verify Kim's conjecture in a range of new cases.

Original languageEnglish
Pages (from-to)5291-5354
Number of pages64
JournalInternational Mathematics Research Notices
Issue number17
StatePublished - 1 Jan 2016
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)


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