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摘要翻译：
设G是半局部环K上定义的约化仿射群格式。假设要么G是半单的，要么k是正规的、诺以太的。我们证明了G有一个有限的k-子群S，使得自然映射H^1(R，S)-->H^1(R，G)对于每一个含K的半局部环R是满射的。换言之，规范(R)上的G-托子允许将结构约简为S。我们还证明了自然映射H^1(X，S)-->H^1(X，G)在其他几种情形下是满射的，在基环k、方案X/k和群方案G/k上作了适当的假设。这些结果已用于研究环代数以及素特征连通代数群的本质维数。本文最后给出了其他应用。
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英文标题：
《Reduction of structure for torsors over semilocal rings》
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作者：
V. Chernousov, Ph. Gille, Z. Reichstein
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最新提交年份：
2007
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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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一级分类：Mathematics 数学
二级分类：Group Theory 群论
分类描述：Finite groups, topological groups, representation theory, cohomology, classification and structure
有限群、拓扑群、表示论、上同调、分类与结构
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英文摘要：
Let G be a reductive affine group scheme defined over a semilocal ring k. Assume that either G is semisimple or k is normal and noetherian. We show that G has a finite k-subgroup S such that the natural map H^1(R, S) --> H^1(R, G) is surjective for every semilocal ring R containing k. In other words, G-torsors over Spec(R) admit reduction of structure to S. We also show that the natural map H^1(X, S) --> H^1(X, G) is surjective in several other contexts, under suitable assumptions on the base ring k, the scheme X/k and the group scheme G/k. These results have already been used to study loop algebras as well as essential dimension of connected algebraic groups in prime characteristic. Additional applications are presented at the end of this paper.
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PDF链接：
https://arxiv.org/pdf/0710.2064
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