Extensions for finite Chevalley groups III: Rational and generic cohomology

摘要

Let G be a connected reductive algebraic group and B be a Borel subgroup defined over an algebraically closed field of characteristic p > 0. In this paper, the authors study the existence of generic G-cohomology and its stability with rational G-cohomology groups via the use of methods from the authors' earlier work. New results on the vanishing of G and B-cohomology groups are presented. Furthermore, vanishing ranges for the associated finite group cohomology of G(F_q) are established which generalize earlier work of Hiller, in addition to stability ranges for generic cohomology which improve on seminal work of Cline, Parshall, Scott and van der Kallen.