非分歧动机交错多重混合值
Unramified Motivic Alternating Multiple Mixed Values
- Anhui Normal University（安徽师范大学）
- The Bishop’s School（主教学校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究多重混合值的交错版本，利用Brown和Glanois的下降理论识别五族非分歧交错多重混合值，并猜想所有此类值均已被给出。
AI中文摘要：
近年来，多重zeta值的许多变体已被研究。其中有一些仍然是实数，例如由作者定义的作为二级推广的多重混合值，这些值包括Hoffman的多重$t$-值和Kaneko--Tsumura的多重$T$-值。一个核心问题是，这样的值何时下降到一级，即何时可以表示为多重zeta值的$\Q$-线性组合。我们称这些值为非分歧的。在本文中，我们进一步考虑上述变体的交错版本，并利用Brown和Glanois的下降理论识别出五族非分歧交错多重混合值。我们猜想，所有非分歧的真正交错多重混合值都在本文中给出。
英文摘要：
Many variants of the multiple zeta values have been studied in recent years. There are a few among them that remain to be real numbers, such as the multiple mixed values defined by the authors as level-two generalizations, which include both Hoffman's multiple $t$-values and Kaneko--Tsumura's multiple $T$-values. A central question is when such a value descends to level one, that is, when it can be expressed as a $\Q$-linear combination of multiple zeta values. We call these values unramified. In this paper, we further consider the alternating version of the above variants and identify five families of unramified alternating multiple mixed values using the descent theory of Brown and Glanois. We conjecture that all unramified truly alternating multiple mixed values are given in this paper.
