Mixed Tate Motives and the Unit Equation
Mixed Tate Motives and the Unit Equation
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混合泰特动机和单位方程
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
S. Wewers
中科院分区：
文献类型：
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作者：
Ishai Dan;S. Wewers
这是一系列文章的第二部分，专门讨论“明确的查伯蒂·金理论”，以解释三次被刺穿的线条。其最终目标是构造一个单位方程的算法解，其停止将取决于Goncharov关于通过动机迭代积分耗尽混合Tate动机的猜想（在分支方面有所改进），以及Kim关于通过p进迭代积分确定积分点的猜想。在本文中，我们将在开发用于构建算法的基本工具时解释这意味着什么。我们还制定了一个详尽的例子，它超越了之前所理解的案例，并允许我们在一系列新案例中验证Kim的猜想。2010数学学科分类：11D45, 11G55, 14F42。
This is the second installment in a sequence of articles devoted to “explicit ChabautyKim theory” for the thrice punctured line. Its ultimate goal is to construct an algorithmic solution to the unit equation whose halting will be conditional on Goncharov’s conjecture about exhaustion of mixed Tate motives by motivic iterated integrals (refined somewhat with respect to ramification), and on Kim’s conjecture about the determination of integral points via p-adic iterated integrals. In this installment we explain what this means while developing basic tools for the construction of the algorithm. We also work out an elaborate example, which goes beyond the cases that were understood before, and allows us to verify Kim’s conjecture in a range of new cases. 2010 Mathematics Subject Classification: 11D45, 11G55, 14F42.