几何不变理论中的闭轨道与一致S-不稳定性
Closed Orbits and uniform S-instability in Geometric Invariant Theory
摘要：
本文研究了约化群$G$在仿射簇$V$上的作用.我们证明了关于$V$中的$G$ -轨道的一些一般合理性结果。此外，我们扩展了Kempf和Hesselink关于$G$的最佳不稳定抛物子群的基本结果，这样的一般$G$ -行动。我们应用我们的一般合理性的结果来回答一个问题的塞尔有关的行为，他的概念的$G$ -完全reductionunder可分离的域扩张。我们的新的最优性结果的应用程序还包括一个建设，使我们能够关联到一个最佳的不稳定抛物子群的$G$的任何子群的$G$。最后，我们使用这些新的最优性技术提供了一个特殊情况下的山雀中心猜想的答案。
英文摘要：
In this paper we consider various problems involving the action of a reductive group $G$ on an affine variety $V$. We prove some general rationality results about the $G$-orbits in $V$. In addition, we extend fundamental results of Kempf and Hesselink regarding optimal destabilizing parabolic subgroups of $G$ for such general $G$-actions. We apply our general rationality results to answer a question of Serre concerning the behaviour of his notion of $G$-complete reducibility under separable field extensions. Applications of our new optimality results also include a construction which allows us to associate an optimal destabilizing parabolic subgroup of $G$ to any subgroup of $G$. Finally, we use these new optimality techniques to provide an answer to Tits' Centre Conjecture in a special case.
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