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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The polylog quotient and the Goncharov quotient in computational Chabauty–Kim theory II
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by Ishai Dan-Cohen and David Corwin PDF
Trans. Amer. Math. Soc. 373 (2020), 6835-6861 Request permission

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 $\operatorname {Spec}\mathbb {Z}$. 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.
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Additional Information
  • Ishai Dan-Cohen
  • Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, Be’er Sheva, Israel
  • MR Author ID: 999259
  • Email: ishaidc@gmail.com
  • David Corwin
  • Affiliation: Department of Mathematics, 970 Evans Hall #3840, University of California, Berkeley, Berkeley, California 94720-3840
  • MR Author ID: 1073361
  • Email: corwind@alum.mit.edu
  • Received by editor(s): December 12, 2018
  • Received by editor(s) in revised form: April 23, 2019
  • Published electronically: August 6, 2020
  • Additional Notes: The first author was supported by ISF grant 87590021.
    The second author was supported by NSF RTG grant 1646385, by NSF grants DMS-1069236 and DMS-1601946 (to Bjorn Poonen), and by Simons Foundation grant #402472 (to Bjorn Poonen).
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 6835-6861
  • MSC (2010): Primary 11G55, 14F35, 14F42, 14G05; Secondary 14F30
  • DOI: https://doi.org/10.1090/tran/7964
  • MathSciNet review: 4155193