论文标题
$ \ mathbb {z} [1/2] $上的混合泰特动机的动机Galois组及其在$ \ mathbb {p}^{1} \ setMinus \ setminus \ {0，\ pm1，\ pm1，\ pm1，\ pm1，\ pm1，\ infty \} $的基本组上的动作
The motivic Galois group of mixed Tate motives over $\mathbb{Z}[1/2]$ and its action on the fundamental group of $\mathbb{P}^{1}\setminus\{0,\pm1,\infty\}$
论文作者
论文摘要
在本文中，我们介绍了动机欧拉总和（也称为交替的多个Zeta值）的汇合关系，并表明汇合关系耗尽了动机Euler总和之间的所有线性关系。这确定了$ \ Mathbb {p}^{1} \ setMinus \ {0，\ pm1，\ pm1，\ infty \} $的de rham基本群体的所有自动形态。此外，我们还讨论了汇合关系的其他应用，例如明确的$ \ mathbb {q} $ - 通过其基础来对给定的动机欧拉总和进行线性扩展，以及扩展中系数的$ 2 $ - 亚基完整性。
In this paper we introduce confluence relations for motivic Euler sums (also called alternating multiple zeta values) and show that all linear relations among motivic Euler sums are exhausted by the confluence relations. This determines all automorphisms of the de Rham fundamental groupoid of $\mathbb{P}^{1}\setminus\{0,\pm1,\infty\}$ coming from the action of the motivic Galois group of mixed Tate motives over $\mathbb{Z}[1/2]$. Moreover, we also discuss other applications of the confluence relations such as an explicit $\mathbb{Q}$-linear expansion of a given motivic Euler sum by their basis and $2$-adic integrality of the coefficients in the expansion.
