AI 中文总结
本文证明Bondarko等人构造的KGL-模同伦范畴上Chow权重结构的心，等价于Gillet等引入的K₀-动机范畴，通过研究Borel-Moore理论与代数G-理论乘积的Tor-运算公式完成证明。
AI 中文摘要
Bondarko和Luzgarev在KGL-模的同伦范畴上构造了Chow权重结构；我们证明该权重结构的心等价于Gillet与Soulé引入的K₀-动机范畴，它是Corti与Hanamura定义的相对Chow动机范畴的K-理论对应物。该证明通过详细研究KGL-模中的Borel-Moore理论，以及代数G-理论中乘积基于Tor-运算的显式公式完成。
英文摘要
Bondarko and Luzgarev constructed the Chow weight structure on the homotopy category of $KGL$-modules; we show that the heart of this weight structure is equivalent to the category of $K_0$-motives introduced by Gillet and Soulé, which is the $K$-theoretic counterpart of the category of relative Chow motives defined by Corti and Hanamura. The proof is achieved via a detailed study on the Borel-Moore theory in $KGL$-modules, as well as explicit formulas for products in algebraic $G$-theory in terms of $\operatorname{Tor}$-operations.
