摘要翻译:
设G是域K上的半单代数群。引入G的高Tits指数作为G在所有域扩张K/K上的所有Tits指数的集合。在二次型的上下文中,这个概念与M.Knebusch提出并由N.Karpenko和A.Vishik分类的更高Witt指数的概念相吻合。我们对例外代数群的高Tits指数进行了分类。我们的主要工具涉及Chow群和投射齐次簇的Chow动机、Steenrod运算以及代数群的J-不变量的概念。
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英文标题:
《Higher Tits indices of algebraic groups》
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作者:
Viktor Petrov, Nikita Semenov
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最新提交年份:
2008
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分类信息:
一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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英文摘要:
Let G be a semisimple algebraic group over a field k. We introduce the higher Tits indices of G as the set of all Tits indices of G over all field extensions K/k. In the context of quadratic forms this notion coincides with the notion of the higher Witt indices introduced by M. Knebusch and classified by N. Karpenko and A. Vishik. We classify the higher Tits indices for exceptional algebraic groups. Our main tools involve the Chow groups and the Chow motives of projective homogeneous varieties, Steenrod operations, and the notion of the J-invariant of algebraic groups.
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PDF链接:
https://arxiv.org/pdf/0706.2827