The polylog quotient and the goncharov quotient in computational chabauty-kim theory II

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Abstract

This is the second installment in a multi-part series starting with Corwin-Dan-Cohen [arXiv:1812.05707v3]. Building on previous work by Dan-Cohen-Wewers, Dan-Cohen, and F. Brown, we push the computational boundary of our explicit motivic version of Kim's method in the case of the thrice punctured line over an open subscheme of Spec Z. To do so, we develop a refined version of the algorithm of Dan-Cohen-Wewers tailored specifically to this case. We also commit ourselves fully to working with the polylogarithmic quotient. This allows us to restrict our calculus with motivic iterated integrals to the so-called depth-1 part of the mixed Tate Galois group studied extensively by Goncharov. An application was given in Corwin-Dan-Cohen [arXiv:1812.05707v3], where we verified Kim's conjecture in an interesting new case.

Original languageEnglish
Pages (from-to)6835-6861
Number of pages27
JournalTransactions of the American Mathematical Society
Volume373
Issue number10
DOIs
StatePublished - 1 Oct 2020

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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