Vol. 14, No. 5, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 6, 1331–1667
Issue 5, 1055–1329
Issue 4, 815–1054
Issue 3, 545–813
Issue 2, 275–544
Issue 1, 1–274

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
Mixed Tate motives and the unit equation II

Ishai Dan-Cohen

Vol. 14 (2020), No. 5, 1175–1237

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.

mixed Tate motives, unipotent fundamental group, p-adic periods, polylogarithms, unit equation, integral points
Mathematical Subject Classification 2010
Primary: 11G55
Secondary: 11D45, 14F30, 14F35, 14F42, 14G05
Received: 10 October 2018
Revised: 16 September 2019
Accepted: 27 November 2019
Published: 13 July 2020
Ishai Dan-Cohen
Department of Mathematics
Ben Gurion University
Be’er Sheva