@article{5eb07b1cc9ab4e0f8022f995d135f221,
title = "Mixed tate motives and the unit equation II",
abstract = "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{\textquoteright}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.",
keywords = "Integral points, Mixed Tate motives, P-adic periods, Polylogarithms, Unipotent fundamental group, Unit equation",
author = "Ishai Dan-Cohen",
note = "Funding Information: This work was supported by Priority Program 1489 of the Deutsche Forschungsgemeinschaft: Experimental and algorithmic methods in algebra, geometry, and number theory.I would like to thank Stefan Wewers for helpful conversations during the conference on multiple zeta values in Madrid in December of 2014. I would like to thank Minhyong Kim, Amnon Besser, Francis Brown, Francesc Fit{\'e}, Go Yamashita for helpful conversations and email exchanges. I would like to thank Cl{\'e}ment Dupont for long conversations during our time in Sarrians, and for pointing out a very helpful counterexample (see the appendix). I would like to thank Rodolfo Venerucci for conversations about finite cohomology. I would like to thank Jochen Heinloth and Giuseppe Ancona for help improving my presentation of the results. I would like to thank David Corwin for a careful reading and many helpful comments; moreover, in the course of our joint work [Corwin and Dan-Cohen 2018a], we discovered that Conjecture 2.1.4 was false as stated in a previous draft. Finally, I wish to thank the referees for their helpful comments and suggestions. Funding Information: This work was supported by Priority Program 1489 of the Deutsche Forschungsgemeinschaft: Experimental and algorithmic Publisher Copyright: {\textcopyright} 2020, Mathematical Sciences Publishers. All rights reserved.",
year = "2020",
month = jan,
day = "1",
doi = "10.2140/ant.2020.14.1175",
language = "English",
volume = "14",
pages = "1175--1237",
journal = "Algebra and Number Theory",
issn = "1937-0652",
publisher = "Mathematical Sciences Publishers",
number = "5",
}