Support varieties for infinitesimal group schemes

Abstract

The representation theory of a connected smooth affine group scheme over a field k of characteristic p > 0 is faithfully captured by that of its family of Frobenius kernels. Such Frobenius kernels are examples of infinitesimal group schemes, affine group schemes G whose coordinate (Hopf) algebra k[G] is a finite-dimensional local k-algebra. This paper presents a study of the cohomology algebra H * (G, k) of an arbitrary infinitesimal group scheme over k.