动机李代数可嵌入一般线性群的上同调
The motivic Lie algebra embeds into the cohomology of the general linear group
AI总结：
该研究证明整数环上混合 Tate 动机的动机李代数可典范嵌入 GL_g(ℤ) 及 𝒜_g 的紧支上同调，通过热带几何等构造，结合相关理论得出图上同调对应动机李代数生成元，还计算了边数≤14 的图的典范图上同调。
AI中文摘要：
我们证明，整数环上混合 Tate 动机的动机李代数可典范嵌入 GL_g(ℤ) 的局部对称空间的不稳定紧支上同调，以及主极化阿贝尔簇的模空间 𝒜_g 的权零紧支上同调。我们的构造通过热带几何与复形实现：Borel 类的紧支类似物经热带 Torelli 映射拉回为典范图上同调，这类上同调最近被认定为 Rossi 和 Willwacher 此前研究过的上同调。我们结合他们的结果与单值周期理论，得出这类上同调映射到动机李代数的生成元。我们还计算了所有边数≤14 的图对应的典范图上同调。
英文摘要：
We show that the motivic Lie algebra of mixed Tate motives over $\mathbb{Z}$ embeds canonically into the unstable compactly-supported cohomology of locally symmetric spaces for $\mathrm{GL}_g(\mathbb{Z})$, and into the weight-zero compactly-supported cohomology of $\mathcal{A}_g$, the moduli space of principally polarized abelian varieties. Our construction passes through tropical geometry and graph complexes: compactly-supported analogues of the Borel classes pull back via the tropical Torelli map to canonical graph cocycles. The latter were recently identified with cocycles studied previously by Rossi and Willwacher. We combine their results with the theory of single-valued periods to conclude that the cocycles map to generators of the motivic Lie algebra. We also compute the canonical graph cocycles for all graphs with $\leq14$ edges.
