多重齐次协变在有限群本质维数中的应用
Application of Multihomogeneous Covariants to the Essential Dimension of Finite Groups
摘要：
本文研究了任意域上有限群的本质维数，并给出了由H.Kraft，G.Schwarz和作者提出的多重均匀化的系统处理。我们推广了Buhler和Reichstein的中心扩张定理，并用多重均匀化代替和推广了Karpenko和Merkurjev关于p-群的本质维数的定理中涉及栈的部分.本文的一部分致力于研究完全可约忠实表示。其中的结果有关忠实表示的最小尺寸有一个计算的最小数目的不可约组件需要一个忠实的表示。
英文摘要：
We investigate essential dimension of finite groups over arbitrary fields and give a systematic treatment of multihomogenization, introduced by H.Kraft, G.Schwarz and the author. We generalize the central extension theorem of Buhler and Reichstein and use multihomogenization to substitute and generalize the stack-involved part of the theorem of Karpenko and Merkurjev about the essential dimension of p-groups. One part of this paper is devoted to the study of completely reducible faithful representations. Amongst results concerning faithful representations of minimal dimension there is a computation of the minimal number of irreducible components needed for a faithful representation.
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