Application of Multihomogeneous Covariants to the Essential Dimension of Finite Groups

Abstract

We investigate essential dimension of finite groups over arbitrary fields and give a systematic treatment of multihomogenization, introduced in [KLS08]. We generalize the central extension theorem of Buhler and Reichstein, [BR97, Theorem 5.3] and use multihomogenization to substitute and generalize the stack-involved part of the theorem of Karpenko and Merkurjev [KM08] 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.

Cite this paper

@inproceedings{Ltscher2008ApplicationOM, title={Application of Multihomogeneous Covariants to the Essential Dimension of Finite Groups}, author={Roland L{\"{o}tscher}, year={2008} }