论文标题
$ \ mathbb a^1 $连接的还原组件的强度$ \ mathbb a^1 $ invariance
Strong $\mathbb A^1$-invariance of $\mathbb A^1$-connected components of reductive algebraic groups
论文作者
论文摘要
我们表明，在完美字段上，$ \ mathbb a^1 $连接的组件的捆绑组件强烈$ \ mathbb a^1 $ invariant。结果，此类组下的Torsors产生了$ \ Mathbb a^1 $ - 纤维序列。 We also show that sections of $\mathbb A^1$-connected components of anisotropic, semisimple, simply connected algebraic groups over an arbitrary field agree with their $R$-equivalence classes, thereby removing the perfectness assumption in the previously known results about the characterization of isotropy in terms of affine homotopy invariance of Nisnevich locally trivial torsors.
We show that the sheaf of $\mathbb A^1$-connected components of a reductive algebraic group over a perfect field is strongly $\mathbb A^1$-invariant. As a consequence, torsors under such groups give rise to $\mathbb A^1$-fiber sequences. We also show that sections of $\mathbb A^1$-connected components of anisotropic, semisimple, simply connected algebraic groups over an arbitrary field agree with their $R$-equivalence classes, thereby removing the perfectness assumption in the previously known results about the characterization of isotropy in terms of affine homotopy invariance of Nisnevich locally trivial torsors.
