标题： 一个动机的几何分裂$\textrm{GL}_n$ 显示英文标题

标题： A Geometric Splitting of the Motive of $\textrm{GL}_n$

摘要： 一篇由海恩斯·米勒撰写的论文表明，在单位群上存在一个滤过结构，该结构在稳定同伦范畴中分解，其中稳定子项是某些Grassmannian上的Thom空间。 我们在弗沃德斯基的稳定动机复形张量三角范畴$\textbf{DM}(k,R)$中给出了这个结果的代数版本，其中$k$是一个域。 具体来说，我们展示了米勒分解中出现的Thom空间的代数类似物，这些类似物在$\textbf{DM}(k,R)$中导致了动机$M(\textrm{GL}_n)$的类似分解，其中$\textrm{GL}_n$是在$k$上的通用线性群概形。 显示英文摘要

摘要： A paper by Haynes Miller shows that there is a filtration on the unitary groups that splits in the stable homotopy category, where the stable summands are certain Thom spaces over Grassmannians. We give an algebraic version of this result in the context of Voevodsky's tensor triangulated category of stable motivic complexes $\textbf{DM}(k,R)$, where $k$ is a field. Specifically, we show that there are algebraic analogs of the Thom spaces appearing in Miller's splitting that give rise to an analogous splitting of the motive $M(\textrm{GL}_n)$ in $\textbf{DM}(k,R)$, where $\textrm{GL}_n$ is the general linear group scheme over $k$.