AI 中文总结
本文定义初始动机三角范畴，通过Chow权结构证明各向同性局部化族保守且Pic-内射，推广了混合设定下高阶Tate迹的研究。
AI 中文摘要
本文定义了初始动机的三角范畴，该范畴包含例如所有内型半单代数群的射影齐次簇的动机。通过分析其Chow权结构，我们证明了由基域的有限生成扩张索引的各向同性局部化族在初始动机上是保守的且Pic-内射的。这一结果在混合设定中推广了Quéguiner-Mathieu和第一作者关于Chow动机的高阶Tate迹的工作。
英文摘要
In this paper, we define the triangulated category of initial motives, which contains, for example, all motives of projective homogeneous varieties for semisimple algebraic groups of inner type. By analyzing its Chow weight structure, we prove that the family of isotropic localizations indexed by finitely generated extensions of the base field is conservative and Pic-injective on initial motives. This result provides an extension, in the mixed setting, of the work of Quéguiner-Mathieu and the first author on higher Tate traces of Chow motives.
