线性连接器组的烧瓶溶液
R'esolutions flasques des groupes lin'eaires connexes
摘要：
域k上的连通约化群G可以写为商H/S，其中k-群H是拟平凡环面通过单连通半单群的扩张，S是以H为中心的flasque k-环面（flasque torus是其余特征标群是H^1-平凡伽罗瓦格的环面）。flasque环面S是明确的乘法准平凡环面。这样的表示G=H/S导致了G的伽罗瓦上同调和相关对象的简化方法，例如G的光滑紧化的Brauer群。当k是一个数域时，人们也恢复了已知的公式，在S方面，有理点群的商由R-等价，并为阿贝尔群，衡量缺乏弱逼近和失败的哈塞原则的主齐性空间。
英文摘要：
A connected reductive group G over a field k may be written as a quotient H/S, where the k-group H is an extension of a quasitrivial torus by a simply connected semisimple group, and S is a flasque k-torus, central in H (a flasque torus is a torus whose cocharacter group is an H^1-trivial Galois lattice). The flasque torus S is well-defined up to multiplication by a quasitrivial torus. Such presentations G=H/S lead to a simplified approach of the Galois cohomology of G and of related objects, such as the Brauer group of a smooth compactification of G. When k is a number field, one also recovers known formulas, in terms of S, for the quotient of the group of rational points by R-equivalence, and for the abelian groups which measure the lack of weak approximation and the failure of the Hasse principle for principal homogeneous spaces.
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