论文标题
在$ \ mathbb {a}^1 $ -Euler特征的最大托里在还原组中的特征
On the $\mathbb{A}^1$-Euler characteristic of the variety of maximal tori in a reductive group
论文作者
论文摘要
我们表明，对于一个还原的组$ g $而言，$ k $ $ \ mathbb {a}^1 $ - $ euler特征是$ g $ in $ g $的多种最大托里的特征，这是Grothendieck-witt Ring $ \ Mathrm {gw}（gw}（k）$的薄弱形式的GROTHENDIECK-WITT RING $ \ MATHRM奖励。作为应用程序，我们获得了广义分裂原理，该原理允许一个人减少尼斯内维奇本地微不足道的$ g $ - $ torsor的结构组。
We show that for a reductive group $G$ over a field $k$ the $\mathbb{A}^1$-Euler characteristic of the variety of maximal tori in $G$ is an invertible element of the Grothendieck-Witt ring $\mathrm{GW}(k)$, settling the weak form of a conjecture by Fabien Morel. As an application we obtain a generalized splitting principle which allows one to reduce the structure group of a Nisnevich locally trivial $G$-torsor to the normalizer of a maximal torus.
