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2020 Mixed Tate motives and the unit equation II
Ishai Dan-Cohen
Algebra Number Theory 14(5): 1175-1237 (2020). DOI: 10.2140/ant.2020.14.1175

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’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.

Citation

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Ishai Dan-Cohen. "Mixed Tate motives and the unit equation II." Algebra Number Theory 14 (5) 1175 - 1237, 2020. https://doi.org/10.2140/ant.2020.14.1175

Information

Received: 10 October 2018; Revised: 16 September 2019; Accepted: 27 November 2019; Published: 2020
First available in Project Euclid: 17 September 2020

zbMATH: 07244793
MathSciNet: MR4129385
Digital Object Identifier: 10.2140/ant.2020.14.1175

Subjects:
Primary: 11G55
Secondary: 11D45 , 14F30 , 14F35 , 14F42 , 14G05

Keywords: Integral points , mixed Tate motives , p-adic periods , polylogarithms , unipotent fundamental group , unit equation

Rights: Copyright © 2020 Mathematical Sciences Publishers

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