On comparing the cohomology of algebraic groups, finite Chevalley groups and Frobenius kernels

✍ Scribed by Christopher P. Bendel; Daniel K. Nakano; Cornelius Pillen

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 225 KB
• Volume: 163
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(01)00024-x

✦ Synopsis

Let G be a semisimple simply connected algebraic group deÿned and split over the ÿeld Fp with p elements, G(Fq) be the ÿnite Chevalley group consisting of the Fq-rational points of G where q = p r , and Gr be the rth Frobenius kernel of G. This paper investigates relationships between the extension theories of G, G(Fq), and Gr over the algebraic closure of Fp. First, some qualitative results relating extensions over G(Fq) and Gr are presented. Then certain extensions over G(Fq) and Gr are explicitly identiÿed in terms of extensions over G.