| Using a recent result of Friedlander and Suslin about finite-generation of cohomology, we develop a theory of support varieties for infinitesimal algebraic groups. More precisely, we consider Frobenius kernels of algebraic k-group schemes defined over the prime field F;In order to identify these varieties, we construct a finite map from the varieties to affine space and then identify the image under this map. We first give a thorough discussion of the additive group, the results for which are then used in the identification for more general groups. For the trivial module, the complete identification for the general linear group is due to Suslin. We present a partial proof and then use this identification to identify the images for some of the classical subgroups. We then discuss the images of support subvarieties for nontrivial modules, and lastly present some applications of these identifications. |
