Mixed Tate motives and the unit equation II
| Autor: | Ishai Dan-Cohen |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
unipotent fundamental group
Rational number Fundamental group mixed Tate motives 14F35 11D45 01 natural sciences 14F30 Set (abstract data type) Mathematics - Algebraic Geometry 0103 physical sciences FOS: Mathematics 14G05 Number Theory (math.NT) 0101 mathematics Algebraic Geometry (math.AG) Mathematics 14F42 Algebra and Number Theory Series (mathematics) Mathematics - Number Theory 11G55 010102 general mathematics integral points Construct (python library) Algebraic number field Algebra Line (geometry) p-adic periods 010307 mathematical physics polylogarithms unit equation Unit (ring theory) |
| Zdroj: | Algebra Number Theory 14, no. 5 (2020), 1175-1237 |
| DOI: | 10.48550/arxiv.1510.01362 |
| Popis: | 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 in the last installment, we construct an algorithm whose output upon halting is provably the set of integral points, and whose halting would follow from conjectures. Our results go a long way towards achieving our goals over the rationals, while broaching the topic of higher number fields. Comment: The "realization algorithm" of previous versions contained an error, so has been substantially reworked in section 3.7. Numerous inaccuracies in my account of the numerical approximation algorithm have been corrected in section 6. Finally, the Hasse principle in Galois cohomology of Condition 2.2.13 is now shown to follow from a conjecture due to Jannsen. To appear in Algebra and Number Theory |
| Databáze: | OpenAIRE |
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